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100-719: The north magnetic pole moves over time according to magnetic changes and flux lobe elongation in the Earth's outer core . In 2001, it was determined by the Geological Survey of Canada to lie west of Ellesmere Island in northern Canada at 81°18′N 110°48′W  /  81.300°N 110.800°W  / 81.300; -110.800  ( Magnetic North Pole 2001 ) . It was situated at 83°06′N 117°48′W  /  83.100°N 117.800°W  / 83.100; -117.800  ( Magnetic North Pole 2005 est ) in 2005. In 2009, while still situated within

200-792: A South Pole expedition . He left Norway in June 1910 on the ship Fram and reached Antarctica in January 1911. His party established a camp at the Bay of Whales and a series of supply depots on the Barrier (now known as the Ross Ice Shelf ) before setting out for the pole in October. The party of five, led by Amundsen, became the first to reach the South Pole on 14 December 1911. Following

300-434: A continuous body , a deformation field results from a stress field due to applied forces or because of some changes in the conditions of the body. The relation between stress and strain (relative deformation) is expressed by constitutive equations , e.g., Hooke's law for linear elastic materials. Deformations which cease to exist after the stress field is removed are termed as elastic deformation . In this case,

400-461: A compass. In North America the line of zero declination (the agonic line ) runs from the north magnetic pole down through Lake Superior and southward into the Gulf of Mexico (see figure). Along this line, true north is the same as magnetic north. West of the agonic line a compass will give a reading that is east of true north and by convention the magnetic declination is positive. Conversely, east of

500-432: A current or deformed configuration κ t ( B ) (Figure 1). If after a displacement of the continuum there is a relative displacement between particles, a deformation has occurred. On the other hand, if after displacement of the continuum the relative displacement between particles in the current configuration is zero, then there is no deformation and a rigid-body displacement is said to have occurred. The vector joining

600-403: A curve in the final placement. If none of the curves changes length, it is said that a rigid body displacement occurred. It is convenient to identify a reference configuration or initial geometric state of the continuum body which all subsequent configurations are referenced from. The reference configuration need not be one the body actually will ever occupy. Often, the configuration at t = 0

700-505: A doctor, a promise that Amundsen kept until his mother died when he was aged 21. He promptly quit university for a life at sea. Amundsen was in the Uranienborg neighbourhood an occasional childhood playmate of the pioneering Antarctica explorer Carsten Borchgrevink . When he was fifteen years old, Amundsen was enthralled by reading Sir John Franklin 's narratives of his overland Arctic expeditions. Amundsen wrote "I read them with

800-586: A failed attempt in 1918 to reach the North Pole by traversing the Northeast Passage on the ship Maud , Amundsen began planning for an aerial expedition instead. On 12 May 1926, Amundsen and 15 other men in the airship Norge became the first explorers verified to have reached the North Pole. Amundsen disappeared in June 1928 while flying on a rescue mission for the airship Italia in

900-615: A fervid fascination which has shaped the whole course of my life". Amundsen joined the Belgian Antarctic Expedition as first mate at the age of 25 in 1897. This expedition, led by Adrien de Gerlache using the ship the RV Belgica , became the first expedition to overwinter in Antarctica. The Belgica , whether by mistake or design, became locked in the sea ice at 70°30′S off Alexander Island , west of

1000-459: A hypothetical "magnetic island" somewhere in the far north (see Rupes Nigra ), or to Polaris , the pole star . The idea that Earth itself acts as essentially a giant magnet was first proposed in 1600, by the English physician and natural philosopher William Gilbert . He was also the first to define the north magnetic pole as the point where Earth's magnetic field points vertically downwards. This

1100-414: A new ship, Maud , lasted until 1925. Maud was carefully navigated through the ice west to east through the Northeast Passage . With him on this expedition were Oscar Wisting and Helmer Hanssen, both of whom had been part of the team to reach the South Pole. In addition, Henrik Lindstrøm was included as a cook. He suffered a stroke and was so physically reduced that he could not participate. The goal of

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1200-402: A quarrel within the group, and Amundsen sent Johansen and the other two men to explore King Edward VII Land . A second attempt, with a team of five made up of Olav Bjaaland , Helmer Hanssen , Sverre Hassel , Oscar Wisting and Amundsen, departed base camp on 19 October. They took four sledges and 52 dogs. Using a route along the previously unknown Axel Heiberg Glacier , they arrived at

1300-428: A straight line drawn from one to the other does not pass through the geometric center of Earth. Earth's north and south magnetic poles are also known as magnetic dip poles , with reference to the vertical "dip" of the magnetic field lines at those points. All magnets have two poles, where lines of magnetic flux enter one pole and emerge from the other pole. By analogy with Earth's magnetic field, these are called

1400-2169: Is a special affine deformation that does not involve any shear, extension or compression. The transformation matrix F is proper orthogonal in order to allow rotations but no reflections . A rigid body motion can be described by x ( X , t ) = Q ( t ) ⋅ X + c ( t ) {\displaystyle \mathbf {x} (\mathbf {X} ,t)={\boldsymbol {Q}}(t)\cdot \mathbf {X} +\mathbf {c} (t)} where Q ⋅ Q T = Q T ⋅ Q = 1 {\displaystyle {\boldsymbol {Q}}\cdot {\boldsymbol {Q}}^{T}={\boldsymbol {Q}}^{T}\cdot {\boldsymbol {Q}}={\boldsymbol {\mathit {1}}}} In matrix form, [ x 1 ( X 1 , X 2 , X 3 , t ) x 2 ( X 1 , X 2 , X 3 , t ) x 3 ( X 1 , X 2 , X 3 , t ) ] = [ Q 11 ( t ) Q 12 ( t ) Q 13 ( t ) Q 21 ( t ) Q 22 ( t ) Q 23 ( t ) Q 31 ( t ) Q 32 ( t ) Q 33 ( t ) ] [ X 1 X 2 X 3 ] + [ c 1 ( t ) c 2 ( t ) c 3 ( t ) ] {\displaystyle {\begin{bmatrix}x_{1}(X_{1},X_{2},X_{3},t)\\x_{2}(X_{1},X_{2},X_{3},t)\\x_{3}(X_{1},X_{2},X_{3},t)\end{bmatrix}}={\begin{bmatrix}Q_{11}(t)&Q_{12}(t)&Q_{13}(t)\\Q_{21}(t)&Q_{22}(t)&Q_{23}(t)\\Q_{31}(t)&Q_{32}(t)&Q_{33}(t)\end{bmatrix}}{\begin{bmatrix}X_{1}\\X_{2}\\X_{3}\end{bmatrix}}+{\begin{bmatrix}c_{1}(t)\\c_{2}(t)\\c_{3}(t)\end{bmatrix}}} A change in

1500-888: Is common to superimpose the coordinate systems for the undeformed and deformed configurations, which results in b = 0 , and the direction cosines become Kronecker deltas : E J ⋅ e i = δ J i = δ i J {\displaystyle \mathbf {E} _{J}\cdot \mathbf {e} _{i}=\delta _{Ji}=\delta _{iJ}} Thus, we have u ( X , t ) = x ( X , t ) − X or u i = x i − δ i J X J = x i − X i {\displaystyle \mathbf {u} (\mathbf {X} ,t)=\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \qquad {\text{or}}\qquad u_{i}=x_{i}-\delta _{iJ}X_{J}=x_{i}-X_{i}} or in terms of

1600-402: Is considered the reference configuration, κ 0 ( B ) . The configuration at the current time t is the current configuration . For deformation analysis, the reference configuration is identified as undeformed configuration , and the current configuration as deformed configuration . Additionally, time is not considered when analyzing deformation, thus the sequence of configurations between

1700-431: Is continuity during deformation of a continuum body in the sense that: An affine deformation is a deformation that can be completely described by an affine transformation . Such a transformation is composed of a linear transformation (such as rotation, shear, extension and compression) and a rigid body translation. Affine deformations are also called homogeneous deformations . Therefore, an affine deformation has

1800-738: Is defined as an isochoric plane deformation in which there is a set of line elements with a given reference orientation that do not change length and orientation during the deformation. If e 1 is the fixed reference orientation in which line elements do not deform during the deformation then λ 1 = 1 and F · e 1 = e 1 . Therefore, F 11 e 1 + F 21 e 2 = e 1 ⟹ F 11 = 1   ;     F 21 = 0 {\displaystyle F_{11}\mathbf {e} _{1}+F_{21}\mathbf {e} _{2}=\mathbf {e} _{1}\quad \implies \quad F_{11}=1~;~~F_{21}=0} Since

1900-569: Is little evidence, it was said that Amundsen had a brief affair with his landlady in Antwerp —until he came home and found her dead after an apparent suicide. His biographer Tor Bomann-Larsen also suggests a romantic relationship between Amundsen and Sigrid Castberg, wife of the lawyer Leif Castberg from Gjøvik , in the years before the South Pole expedition, a relationship Amundsen broke off after that expedition in favour of Kiss Bennett. Author Julian Sancton noted that in his younger years, Amundsen

2000-485: Is north, then what we call the Earth's north magnetic pole is actually its south magnetic pole since it attracts the north magnetic pole of other magnets, such as compass needles. The direction of magnetic field lines is defined such that the lines emerge from the magnet's north pole and enter into the magnet's south pole. Early European navigators, cartographers and scientists believed that compass needles were attracted to

2100-405: Is now drifting away from North America and toward Siberia. Over the life of Earth, the orientation of Earth's magnetic field has reversed many times, with magnetic north becoming magnetic south and vice versa – an event known as a geomagnetic reversal . Evidence of geomagnetic reversals can be seen at mid-ocean ridges where tectonic plates move apart and the seabed is filled in with magma . As

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2200-564: Is quantified as the residual displacement of particles in a non- rigid body , from an initial configuration to a final configuration, excluding the body's average translation and rotation (its rigid transformation ). A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads , intrinsic activity (e.g. muscle contraction ), body forces (such as gravity or electromagnetic forces ), or changes in temperature, moisture content, or chemical reactions, etc. In

2300-1580: Is the deformation gradient tensor . Similarly, the partial differentiation of the displacement vector with respect to the spatial coordinates yields the spatial displacement gradient tensor ∇ x U . Thus we have, U ( x , t ) = x − X ( x , t ) ∇ x U = I − ∇ x X ∇ x U = I − F − 1 {\displaystyle {\begin{aligned}\mathbf {U} (\mathbf {x} ,t)&=\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\\\nabla _{\mathbf {x} }\mathbf {U} &=\mathbf {I} -\nabla _{\mathbf {x} }\mathbf {X} \\\nabla _{\mathbf {x} }\mathbf {U} &=\mathbf {I} -\mathbf {F} ^{-1}\end{aligned}}} or U J = δ J i x i − X J = x J − X J ∂ U J ∂ x k = δ J k − ∂ X J ∂ x k {\displaystyle {\begin{aligned}U_{J}&=\delta _{Ji}x_{i}-X_{J}=x_{J}-X_{J}\\{\frac {\partial U_{J}}{\partial x_{k}}}&=\delta _{Jk}-{\frac {\partial X_{J}}{\partial x_{k}}}\end{aligned}}} Homogeneous (or affine) deformations are useful in elucidating

2400-510: Is the angle of rotation and λ 1 , λ 2 are the principal stretches . If the deformation is isochoric (volume preserving) then det( F ) = 1 and we have F 11 F 22 − F 12 F 21 = 1 {\displaystyle F_{11}F_{22}-F_{12}F_{21}=1} Alternatively, λ 1 λ 2 = 1 {\displaystyle \lambda _{1}\lambda _{2}=1} A simple shear deformation

2500-482: Is the current definition, though it would be a few hundred years before the nature of Earth's magnetic field was understood with modern accuracy and precision. The first group to reach the north magnetic pole was led by James Clark Ross , who found it at Cape Adelaide on the Boothia Peninsula on 1 June 1831, while serving on the second arctic expedition of his uncle, Sir John Ross . Roald Amundsen found

2600-1662: Is the linear transformer and c is the translation. In matrix form, where the components are with respect to an orthonormal basis, [ x 1 ( X 1 , X 2 , X 3 , t ) x 2 ( X 1 , X 2 , X 3 , t ) x 3 ( X 1 , X 2 , X 3 , t ) ] = [ F 11 ( t ) F 12 ( t ) F 13 ( t ) F 21 ( t ) F 22 ( t ) F 23 ( t ) F 31 ( t ) F 32 ( t ) F 33 ( t ) ] [ X 1 X 2 X 3 ] + [ c 1 ( t ) c 2 ( t ) c 3 ( t ) ] {\displaystyle {\begin{bmatrix}x_{1}(X_{1},X_{2},X_{3},t)\\x_{2}(X_{1},X_{2},X_{3},t)\\x_{3}(X_{1},X_{2},X_{3},t)\end{bmatrix}}={\begin{bmatrix}F_{11}(t)&F_{12}(t)&F_{13}(t)\\F_{21}(t)&F_{22}(t)&F_{23}(t)\\F_{31}(t)&F_{32}(t)&F_{33}(t)\end{bmatrix}}{\begin{bmatrix}X_{1}\\X_{2}\\X_{3}\end{bmatrix}}+{\begin{bmatrix}c_{1}(t)\\c_{2}(t)\\c_{3}(t)\end{bmatrix}}} The above deformation becomes non-affine or inhomogeneous if F = F ( X , t ) or c = c ( X , t ) . A rigid body motion

2700-447: Is the presence of what we can call the main magnetic pole on northwestern Prince of Wales Island. I have accepted as a purely preliminary value the position latitude 73°N and longitude 100°W. Your value of 73°15'N and 99°45’W is in excellent agreement, and I suggest that you use your value by all means. (The positions were less than 30 km (20 mi) apart.) The Canadian government has made several measurements since, which show that

2800-906: Is then given by u i = α i J U J or U J = α J i u i {\displaystyle u_{i}=\alpha _{iJ}U_{J}\qquad {\text{or}}\qquad U_{J}=\alpha _{Ji}u_{i}} Knowing that e i = α i J E J {\displaystyle \mathbf {e} _{i}=\alpha _{iJ}\mathbf {E} _{J}} then u ( X , t ) = u i e i = u i ( α i J E J ) = U J E J = U ( x , t ) {\displaystyle \mathbf {u} (\mathbf {X} ,t)=u_{i}\mathbf {e} _{i}=u_{i}(\alpha _{iJ}\mathbf {E} _{J})=U_{J}\mathbf {E} _{J}=\mathbf {U} (\mathbf {x} ,t)} It

2900-559: The Top Gear: Polar Special was broadcast on BBC Two in the United Kingdom, in which Jeremy Clarkson , James May , and their support and camera team claimed to be the first people in history to reach the 1996 location of the north magnetic pole in northern Canada by car. Note that they did not reach the actual north magnetic pole, which at the time (2007) had moved several hundred kilometers further north from

3000-590: The Antarctic Peninsula . The crew endured a winter for which they were poorly prepared. By Amundsen's own estimation, the doctor for the expedition, the American Frederick Cook , probably saved the crew from scurvy by hunting for animals and feeding the crew fresh meat. In cases where citrus fruits are lacking, raw meat – particularly offal – from animals often contains enough vitamin C to prevent scurvy. In 1903, Amundsen led

3100-496: The Parry Channel and then south through Peel Sound , James Ross Strait , Simpson Strait and Rae Strait . They spent two winters at King William Island , in the harbor of what is today Gjoa Haven . During this time, Amundsen and the crew learned from the local Netsilik Inuit about Arctic survival skills, which he found invaluable in his later expedition to the South Pole. For example, he learned to use sled dogs for

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3200-584: The Royal Norwegian Navy , tried to fly from Wainwright, Alaska , to Spitsbergen across the North Pole. When their aircraft was damaged, they abandoned the journey. To raise additional funds, Amundsen traveled around the United States in 1924 on a lecture tour. In 1925, accompanied by Lincoln Ellsworth , pilot Hjalmar Riiser-Larsen , flight mechanic Karl Feucht and two other team members, Amundsen took two Dornier Do J flying boats ,

3300-605: The United States Army to undertake the task. An assignment was made in 1946 for the Army Air Forces' recently formed Strategic Air Command to explore the entire Arctic Ocean area. The exploration was conducted by the 46th (later re-designated the 72nd) Photo Reconnaissance Squadron and reported on as a classified Top Secret mission named Project Nanook . This project in turn was divided into many separate, but identically classified, projects, one of which

3400-432: The antipodal points where the axis of this theoretical dipole intersects Earth's surface. If Earth's magnetic field were a perfect dipole then the field lines would be vertical at the geomagnetic poles, and they would coincide with the magnetic poles. However, the approximation is imperfect, and so the magnetic and geomagnetic poles lie some distance apart. Like the north magnetic pole, the north geomagnetic pole attracts

3500-963: The polar decomposition theorem , the deformation gradient, up to a change of coordinates, can be decomposed into a stretch and a rotation. Since all the deformation is in a plane, we can write F = R ⋅ U = [ cos ⁡ θ sin ⁡ θ 0 − sin ⁡ θ cos ⁡ θ 0 0 0 1 ] [ λ 1 0 0 0 λ 2 0 0 0 1 ] {\displaystyle {\boldsymbol {F}}={\boldsymbol {R}}\cdot {\boldsymbol {U}}={\begin{bmatrix}\cos \theta &\sin \theta &0\\-\sin \theta &\cos \theta &0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\lambda _{1}&0&0\\0&\lambda _{2}&0\\0&0&1\end{bmatrix}}} where θ

3600-438: The 1996 position. Historically, the magnetic compass was an important tool for navigation . While it has been widely replaced by Global Positioning Systems , many airplanes and ships still carry them, as do casual boaters and hikers. The direction in which a compass needle points is known as magnetic north. In general, this is not exactly the direction of the north magnetic pole (or of any other consistent location). Instead,

3700-407: The 20th century it moved 1,100 km (680 mi), and since 1970 its rate of motion has accelerated from 9 to 52 km (5.6 to 32.3 mi) per year (2001–2007 average; see also polar drift ). Members of the 2007 expedition to locate the magnetic north pole wrote that such expeditions have become logistically difficult, as the pole moves farther away from inhabited locations. They expect that in

3800-711: The Amundsen flight. Amundsen was a lifelong bachelor, but he had a long-time relationship with the Norwegian-born Kristine Elisabeth ('Kiss') Bennett, the wife of an Englishman, Charles Peto Bennett . He met her in London in 1907 and they remained close for many years; Amundsen kept the relationship a secret from everyone outside his intimate circle. Later, he became engaged to Bess Magids, an American divorcée whom he had met in Alaska. Though there

3900-673: The Arctic in the airship Norge , designed by Nobile. They left Spitsbergen on 11 May 1926, flew over the North Pole on 12 May, and landed in Alaska the following day. The three previous claims to have arrived at the North Pole, by the Americans Frederick Cook in 1908; Robert Peary in 1909; and Richard E. Byrd in 1926 (just a few days before the Norge ) are disputed by some, as being either of dubious accuracy or outrightly fraudulent. If these other claims are false,

4000-458: The Arctic. The search for his remains, which have not been found, was called off that September. Amundsen was born into a family of Norwegian shipowners and captains in Borge , between the towns Fredrikstad and Sarpsborg . His parents were Jens Amundsen and Hanna Sahlqvist. Roald was the fourth son in the family. His mother wanted him to avoid the family maritime trade and encouraged him to become

4100-513: The Barrier, along a line directly south to the Pole. Amundsen also planned to kill most of his dogs on the way and use them as a source for fresh meat. As he went he butchered some of the dogs and fed them to the remaining dogs, as well as eating some himself. A small group, including Hjalmar Johansen , Kristian Prestrud and Jørgen Stubberud , set out on 8 September, but had to abandon their trek due to extreme temperatures. The painful retreat caused

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4200-464: The Canadian Arctic at 84°54′N 131°00′W  /  84.900°N 131.000°W  / 84.900; -131.000  ( Magnetic North Pole 2009 ) , it was moving toward Russia at between 55 and 60 km (34 and 37 mi) per year. In 2013, the distance between the north magnetic pole and the geographic north pole was approximately 800 kilometres (500 mi). As of 2021,

4300-616: The Moon was named after him; the rim of the crater is being considered by NASA as a potential landing location for their Artemis III lunar lander. Built in 1929 and opened in 1930, Amundsen High School opened its doors in Chicago's Ravenswood neighborhood. The 1969 film The Red Tent tells the story of the Nobile expedition and Amundsen's disappearance. Sean Connery plays Amundsen. A book Scott and Amundsen , by Roland Huntford ,

4400-484: The N-24 and N-25, to 87° 44′ north. It was the northernmost latitude reached by plane up to that time. The aircraft landed a few miles apart without radio contact, yet the crews managed to reunite. The N-24 was damaged. Amundsen and his crew worked for more than three weeks to clean up an airstrip to take off from ice. They shovelled 600 tons of ice while consuming only one pound (450 g) of daily food rations. In

4500-514: The North Pole. Amundsen's French Latham 47 flying boat never returned . Later, a wing-float and bottom gasoline tank from the plane, which had been adapted as a replacement wing-float, were found near the Tromsø coast. It is assumed that the plane crashed in the Barents Sea , and that Amundsen and his crew were killed in the wreck, or died shortly afterward. The search for Amundsen and team

4600-673: The Northwest Passage "was a great achievement for Norway". He said he hoped to do more and signed it "Your loyal subject, Roald Amundsen". The crew returned to Oslo in November 1906, after almost three and a half years abroad. Gjøa was returned to Norway in 1972. After a 45-day trip from San Francisco on a bulk carrier, she was placed on land outside the Fram Museum in Oslo, where she is now situated inside her own building at

4700-472: The Norwegian supporters felt misled. Scott was planning his own expedition to the South Pole that year. Using the ship Fram , earlier used by Fridtjof Nansen , Amundsen left Oslo for the south on 3 June 1910. At Madeira , Amundsen alerted his men that they would be heading to Antarctica, and sent a telegram to Scott: "Beg to inform you Fram proceeding Antarctic – Amundsen." Nearly six months later,

4800-490: The Sun. As of early 2019, the magnetic north pole is moving from Canada towards Siberia at a rate of approximately 55 km (34 mi) per year. The NOAA gives the 2024 location of the magnetic north pole as 86 degrees North, 142 degrees East. By 2025, it will have drifted to 138 degrees East (same latitude). The first team of novices to reach the magnetic north pole did so in 1996, led by David Hempleman-Adams . It included

4900-399: The agonic line a compass will point west of true north and the declination is negative. As a first-order approximation , Earth's magnetic field can be modeled as a simple dipole (like a bar magnet), tilted about 10° with respect to Earth's rotation axis (which defines the geographic north and geographic south poles) and centered at Earth's center. The north and south geomagnetic poles are

5000-457: The atomic level. Another type of irreversible deformation is viscous deformation , which is the irreversible part of viscoelastic deformation. In the case of elastic deformations, the response function linking strain to the deforming stress is the compliance tensor of the material. Deformation is the change in the metric properties of a continuous body, meaning that a curve drawn in the initial body placement changes its length when displaced to

5100-430: The behavior of materials. Some homogeneous deformations of interest are Linear or longitudinal deformations of long objects, such as beams and fibers, are called elongation or shortening ; derived quantities are the relative elongation and the stretch ratio . Plane deformations are also of interest, particularly in the experimental context. Volume deformation is a uniform scaling due to isotropic compression ;

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5200-459: The carefully collected scientific data was lost during the ill-fated journey of Peter Tessem and Paul Knutsen , two crew members sent on a mission by Amundsen. The scientific materials were later retrieved in 1922 by Russian scientist Nikolay Urvantsev from where they had been abandoned on the shores of the Kara Sea . The 1923 attempt to fly over the Pole failed. Amundsen and Oskar Omdal , of

5300-533: The command of Wisting, was to resume the original plan to drift over the North Pole in the ice. The ship drifted in the ice for three years east of the New Siberian Islands, never reaching the North Pole. It was finally seized by Amundsen's creditors as collateral for his mounting debt. Although they were unable to reach the North Pole, the scientific results of the expedition, mainly the work of Sverdrup, have proven to be of considerable value. Much of

5400-430: The compass aligns itself to the local geomagnetic field, which varies in a complex manner over Earth's surface, as well as over time. The local angular difference between magnetic north and true north is called the magnetic declination . Most map coordinate systems are based on true north, and magnetic declination is often shown on map legends so that the direction of true north can be determined from north as indicated by

5500-411: The configuration of a continuum body results in a displacement . The displacement of a body has two components: a rigid-body displacement and a deformation. A rigid-body displacement consists of a simultaneous translation and rotation of the body without changing its shape or size. Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration κ 0 ( B ) to

5600-487: The continent and to Hobart , Australia, where Amundsen publicly announced his success on 7 March 1912. He telegraphed news to backers. Amundsen's expedition benefited from his careful preparation, good equipment, appropriate clothing, a simple primary task, an understanding of dogs and their handling, and the effective use of skis. In contrast to the misfortunes of Scott's team, Amundsen's trek proved relatively smooth and uneventful. In 1918, an expedition Amundsen began with

5700-434: The continuum completely recovers its original configuration. On the other hand, irreversible deformations may remain, and these exist even after stresses have been removed. One type of irreversible deformation is plastic deformation , which occurs in material bodies after stresses have attained a certain threshold value known as the elastic limit or yield stress , and are the result of slip , or dislocation mechanisms at

5800-467: The cooperation of many of his squadron teammates in obtaining many hundreds of statistical readings, startling results were revealed: The center of the north magnetic dip pole was on Prince of Wales Island some 400 km (250 mi) NNW of the positions determined by Amundsen and Ross, and the dip pole was not a point but occupied an elliptical region with foci about 400 km (250 mi) apart on Boothia Peninsula and Bathurst Island . Klein called

5900-568: The crew got the ship loose from the ice, but it froze again after eleven days somewhere between the New Siberian Islands and Wrangel Island . During this time, Amundsen suffered a broken arm and was attacked by a polar bear. As a result, he participated little in the work outdoors, such as sleigh rides and hunting. He, Hanssen, and Wisting, along with two other men, embarked on an expedition by dog sled to Nome, Alaska, more than 1,000 kilometres (620 mi) away. But they found that

6000-623: The crew of the Norge would be the first explorers verified to have reached the North Pole, when they floated over it in the Norge in 1926. If the Norge expedition was the first to the North Pole, Amundsen and Oscar Wisting were the first men to have reached both geographical poles, by ground or by air. Amundsen disappeared on 18 June 1928 while flying on a rescue mission in the Arctic. His team included Norwegian pilot Leif Dietrichson , French pilot René Guilbaud , and three more Frenchmen. They were seeking missing members of Nobile's crew, whose new airship Italia had crashed while returning from

6100-535: The crew. During the third winter, Maud was frozen in the western Bering Strait. She finally became free and the expedition sailed south, reaching Seattle , in the American Pacific Northwest in 1921 for repairs. Amundsen returned to Norway, needing to put his finances in order. He took with him two young indigenous girls, a four-year-old he adopted, Kakonita, and her companion Camilla. When Amundsen went bankrupt two years later, however, he sent

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6200-557: The deformation gradient as F = 1 + γ e 1 ⊗ e 2 {\displaystyle {\boldsymbol {F}}={\boldsymbol {\mathit {1}}}+\gamma \mathbf {e} _{1}\otimes \mathbf {e} _{2}} Roald Amundsen This is an accepted version of this page Roald Engelbregt Gravning Amundsen ( UK : / ˈ ɑː m ʊ n d s ən / , US : /- m ə n s -/ ; Norwegian: [ˈrùːɑɫ ˈɑ̂mʉnsən] ; 16 July 1872 – c.  18 June 1928 )

6300-1714: The deformation is isochoric, F 11 F 22 − F 12 F 21 = 1 ⟹ F 22 = 1 {\displaystyle F_{11}F_{22}-F_{12}F_{21}=1\quad \implies \quad F_{22}=1} Define γ := F 12 {\displaystyle \gamma :=F_{12}} Then, the deformation gradient in simple shear can be expressed as F = [ 1 γ 0 0 1 0 0 0 1 ] {\displaystyle {\boldsymbol {F}}={\begin{bmatrix}1&\gamma &0\\0&1&0\\0&0&1\end{bmatrix}}} Now, F ⋅ e 2 = F 12 e 1 + F 22 e 2 = γ e 1 + e 2 ⟹ F ⋅ ( e 2 ⊗ e 2 ) = γ e 1 ⊗ e 2 + e 2 ⊗ e 2 {\displaystyle {\boldsymbol {F}}\cdot \mathbf {e} _{2}=F_{12}\mathbf {e} _{1}+F_{22}\mathbf {e} _{2}=\gamma \mathbf {e} _{1}+\mathbf {e} _{2}\quad \implies \quad {\boldsymbol {F}}\cdot (\mathbf {e} _{2}\otimes \mathbf {e} _{2})=\gamma \mathbf {e} _{1}\otimes \mathbf {e} _{2}+\mathbf {e} _{2}\otimes \mathbf {e} _{2}} Since e i ⊗ e i = 1 {\displaystyle \mathbf {e} _{i}\otimes \mathbf {e} _{i}={\boldsymbol {\mathit {1}}}} we can also write

6400-425: The direction cosines between the material and spatial coordinate systems with unit vectors E J and e i , respectively. Thus E J ⋅ e i = α J i = α i J {\displaystyle \mathbf {E} _{J}\cdot \mathbf {e} _{i}=\alpha _{Ji}=\alpha _{iJ}} and the relationship between u i and U J

6500-1414: The displacement vector with respect to the material coordinates yields the material displacement gradient tensor ∇ X u . Thus we have: u ( X , t ) = x ( X , t ) − X ∇ X u = ∇ X x − I ∇ X u = F − I {\displaystyle {\begin{aligned}\mathbf {u} (\mathbf {X} ,t)&=\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \\\nabla _{\mathbf {X} }\mathbf {u} &=\nabla _{\mathbf {X} }\mathbf {x} -\mathbf {I} \\\nabla _{\mathbf {X} }\mathbf {u} &=\mathbf {F} -\mathbf {I} \end{aligned}}} or u i = x i − δ i J X J = x i − X i ∂ u i ∂ X K = ∂ x i ∂ X K − δ i K {\displaystyle {\begin{aligned}u_{i}&=x_{i}-\delta _{iJ}X_{J}=x_{i}-X_{i}\\{\frac {\partial u_{i}}{\partial X_{K}}}&={\frac {\partial x_{i}}{\partial X_{K}}}-\delta _{iK}\end{aligned}}} where F

6600-626: The edge of the Polar Plateau on 21 November after a four-day climb. The team and 16 dogs arrived at the pole on 14 December, a month before Scott's group. Amundsen named their South Pole camp Polheim . Amundsen renamed the Antarctic Plateau as King Haakon VII's Plateau. They left a small tent and letter stating their accomplishment, in case they did not return safely to Framheim. The team arrived at Framheim on 25 January 1912, with 11 surviving dogs. They made their way off

6700-526: The end, the six crew members were packed into the N-25. In a remarkable feat, Riiser-Larsen took off, and they barely became airborne over the cracking ice. They returned triumphant when everyone thought they had been lost forever. In 1926, Amundsen and 15 other men (including Ellsworth, Riiser-Larsen, Oscar Wisting, and the Italian air crew led by aeronautical engineer Umberto Nobile ) made the first crossing of

6800-559: The expedition arrived at the eastern edge of the Ross Ice Shelf (then known as "the Great Ice Barrier"), at a large inlet called the Bay of Whales , on 14 January 1911. Amundsen established his base camp there, calling it Framheim . Amundsen eschewed the heavy wool clothing worn on earlier Antarctic attempts in favour of adopting Inuit -style furred skins. Using skis and dog sleds for transportation, Amundsen and his men created supply depots at 80°, 81° and 82° South on

6900-469: The expedition told of their relations with Inuit women, and historians have speculated that Amundsen might also have taken a partner, although he wrote a warning against this. Specifically, half-brothers Bob Konona and Paul Ikuallaq say that their father Luke Ikuallaq told them on his deathbed that he was the son of Amundsen. Konona said that their father Ikuallaq was left out on the ice to die after his birth, as his European ancestry made him illegitimate to

7000-501: The expedition was to explore the unknown areas of the Arctic Ocean, strongly inspired by Fridtjof Nansen's earlier expedition with Fram . The plan was to sail along the coast of Siberia and go into the ice farther to the north and east than Nansen had. In contrast to Amundsen's earlier expeditions, this was expected to yield more material for academic research, and he carried the geophysicist Harald Sverdrup on board. The voyage

7100-568: The first British woman Sue Stockdale and first Swedish woman to reach the Pole. The team also successfully tracked the location of the Magnetic North Pole on behalf of the University of Ottawa , and certified its location by magnetometer and theodolite at 78°35′42″N 104°11′54″W  /  78.59500°N 104.19833°W  / 78.59500; -104.19833  ( Magnetic North Pole 1996 ) . The Polar Race

7200-546: The first expedition to traverse Canada's Northwest Passage between the Atlantic and Pacific oceans. He planned a small expedition of six men in a 45-ton fishing vessel, Gjøa , to have flexibility. His ship had relatively shallow draft. His technique was to use a small ship and hug the coast. Amundsen had the ship outfitted with a small 13 horsepower single-screw paraffin (diesel) engine. They traveled via Baffin Bay ,

7300-404: The form x ( X , t ) = F ( t ) ⋅ X + c ( t ) {\displaystyle \mathbf {x} (\mathbf {X} ,t)={\boldsymbol {F}}(t)\cdot \mathbf {X} +\mathbf {c} (t)} where x is the position of a point in the deformed configuration, X is the position in a reference configuration, t is a time-like parameter, F

7400-399: The future, the magnetic pole position will be obtained from satellite data instead of ground surveys. This general movement is in addition to a daily or diurnal variation in which the north magnetic pole describes a rough ellipse, with a maximum deviation of 80 km (50 mi) from its mean position. This effect is due to disturbances of the geomagnetic field by charged particles from

7500-426: The girls to be cared for by Camilla's father, who lived in eastern Russia. In June 1922, Amundsen returned to Maud , which had been sailed to Nome. He decided to shift from the planned naval expedition to aerial ones, and arranged to charter a plane. He divided the expedition team in two: one part, led by him, was to winter over and prepare for an attempt to fly over the pole in 1923. The second team on Maud , under

7600-548: The ice was not frozen solid in the Bering Strait , and it could not be crossed. They sent a telegram from Anadyr to signal their location. After two winters frozen in the ice, without having achieved the goal of drifting over the North Pole, Amundsen decided to go to Nome to repair the ship and buy provisions. Several of the crew ashore there, including Hanssen, did not return on time to the ship. Amundsen considered Hanssen to be in breach of contract, and dismissed him from

7700-429: The magma seeps out of the mantle , cools, and solidifies into igneous rock, it is imprinted with a record of the direction of the magnetic field at the time that the magma cooled. Download coordinates as: Elongation (materials science) In physics and continuum mechanics , deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It

7800-409: The magnet's "north" and "south" poles. Before magnetism was well understood, the north-seeking pole of a magnet was defined to have the north designation, according to their use in early compasses . However, opposite poles attract, which means that as a physical magnet, the magnetic north pole of the Earth is actually on the southern hemisphere. In other words, if we establish that true geographic north

7900-538: The museum. Amundsen next planned to take an expedition to the North Pole and explore the Arctic Basin . Finding it difficult to raise funds, when he heard in 1909 that the Americans Frederick Cook and Robert Peary had claimed to reach the North Pole as a result of two different expeditions, he decided to reroute to Antarctica. He was not clear about his intentions, and Robert F. Scott and

8000-720: The north magnetic pole in a slightly different location in 1903. The third observation was by Canadian government scientists Paul Serson and Jack Clark, of the Dominion Astrophysical Observatory , who found the pole at Allen Lake on Prince of Wales Island in 1947. At the start of the Cold War , the United States Department of War recognized a need for a comprehensive survey of the North American Arctic and asked

8100-468: The north magnetic pole is moving continually northwestward. In 2001, an expedition located the pole at 81°18′N 110°48′W  /  81.300°N 110.800°W  / 81.300; -110.800  ( Magnetic North Pole 2001 ) . In 2007, the latest survey found the pole at 83°57′00″N 120°43′12″W  /  83.95000°N 120.72000°W  / 83.95000; -120.72000  ( Magnetic North Pole 2007 location ) . During

8200-502: The north pole of a bar magnet and so is in a physical sense actually a magnetic south pole. It is the center of the region of the magnetosphere in which the Aurora Borealis can be seen. As of 2015 it was located at approximately 80°22′12″N 72°37′12″W  /  80.37000°N 72.62000°W  / 80.37000; -72.62000  ( Geomagnetic North Pole 2005 est ) , over Ellesmere Island , Canada but it

8300-475: The pole is projected to have moved beyond the Canadian Arctic to 86°24′00″N 156°47′10″E  /  86.400°N 156.786°E  / 86.400; 156.786  ( Magnetic North Pole 2021 est ) . Its southern hemisphere counterpart is the south magnetic pole . Since Earth's magnetic field is not exactly symmetric, the north and south magnetic poles are not antipodal , meaning that

8400-528: The positions of a particle P in the undeformed configuration and deformed configuration is called the displacement vector u ( X , t ) = u i e i in the Lagrangian description, or U ( x , t ) = U J E J in the Eulerian description. A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with

8500-1389: The relative volume deformation is called volumetric strain . A plane deformation, also called plane strain , is one where the deformation is restricted to one of the planes in the reference configuration. If the deformation is restricted to the plane described by the basis vectors e 1 , e 2 , the deformation gradient has the form F = F 11 e 1 ⊗ e 1 + F 12 e 1 ⊗ e 2 + F 21 e 2 ⊗ e 1 + F 22 e 2 ⊗ e 2 + e 3 ⊗ e 3 {\displaystyle {\boldsymbol {F}}=F_{11}\mathbf {e} _{1}\otimes \mathbf {e} _{1}+F_{12}\mathbf {e} _{1}\otimes \mathbf {e} _{2}+F_{21}\mathbf {e} _{2}\otimes \mathbf {e} _{1}+F_{22}\mathbf {e} _{2}\otimes \mathbf {e} _{2}+\mathbf {e} _{3}\otimes \mathbf {e} _{3}} In matrix form, F = [ F 11 F 12 0 F 21 F 22 0 0 0 1 ] {\displaystyle {\boldsymbol {F}}={\begin{bmatrix}F_{11}&F_{12}&0\\F_{21}&F_{22}&0\\0&0&1\end{bmatrix}}} From

8600-436: The spatial coordinate system of reference, are called the spatial coordinates There are two methods for analysing the deformation of a continuum. One description is made in terms of the material or referential coordinates, called material description or Lagrangian description . A second description of deformation is made in terms of the spatial coordinates it is called the spatial description or Eulerian description . There

8700-532: The spatial coordinates as U ( x , t ) = b ( x , t ) + x − X ( x , t ) or U J = b J + α J i x i − X J {\displaystyle \mathbf {U} (\mathbf {x} ,t)=\mathbf {b} (\mathbf {x} ,t)+\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\qquad {\text{or}}\qquad U_{J}=b_{J}+\alpha _{Ji}x_{i}-X_{J}} where α Ji are

8800-508: The spatial coordinates as U ( x , t ) = x − X ( x , t ) or U J = δ J i x i − X J = x J − X J {\displaystyle \mathbf {U} (\mathbf {x} ,t)=\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\qquad {\text{or}}\qquad U_{J}=\delta _{Ji}x_{i}-X_{J}=x_{J}-X_{J}} The partial differentiation of

8900-569: The transport of goods and to wear animal skins in lieu of heavy, woolen parkas, which could not keep out the cold when wet. Leaving Gjoa Haven, he sailed west and passed Cambridge Bay , which had been reached from the west by Richard Collinson in 1852. Continuing to the south of Victoria Island , the ship cleared the Canadian Arctic Archipelago on 17 August 1905 . It had to stop for the winter before going on to Nome on Alaska's Pacific coast. The nearest telegraph station

9000-505: The two foci local poles, for their importance to navigation in emergencies when using a "homing" procedure. About three months after Klein's findings were officially reported, a Canadian ground expedition was sent into the Archipelago to locate the position of the magnetic pole. R. Glenn Madill, Chief of Terrestrial Magnetism, Department of Mines and Resources , Canada, wrote to Lt. Klein on 21 July 1948: … we agree on one point and that

9100-417: The undeformed and deformed configurations are of no interest. The components X i of the position vector X of a particle in the reference configuration, taken with respect to the reference coordinate system, are called the material or reference coordinates . On the other hand, the components x i of the position vector x of a particle in the deformed configuration, taken with respect to

9200-776: The undeformed configuration. It is convenient to do the analysis of deformation or motion of a continuum body in terms of the displacement field. In general, the displacement field is expressed in terms of the material coordinates as u ( X , t ) = b ( X , t ) + x ( X , t ) − X or u i = α i J b J + x i − α i J X J {\displaystyle \mathbf {u} (\mathbf {X} ,t)=\mathbf {b} (\mathbf {X} ,t)+\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \qquad {\text{or}}\qquad u_{i}=\alpha _{iJ}b_{J}+x_{i}-\alpha _{iJ}X_{J}} or in terms of

9300-534: Was 500 mi (800 km) away in Eagle . Amundsen traveled there overland to wire a success message on 5 December, then returned to Nome in 1906. Later that year he was elected to the American Antiquarian Society . Amundsen learned of the dissolution of the union between Norway and Sweden , and that he had a new king. The explorer sent the new king, Haakon VII , news that his traversing

9400-462: Was Project Polaris, which was a radar, photographic ( trimetrogon , or three-angle, cameras) and visual study of the entire Canadian Archipelago . A Canadian officer observer was assigned to accompany each flight. Frank O. Klein, the director of the project, noticed that the fluxgate compass did not behave as erratically as expected—it oscillated no more than 1 to 2 degrees over much of the region—and began to study northern terrestrial magnetism. With

9500-580: Was a Norwegian explorer of polar regions . He was a key figure of the period known as the Heroic Age of Antarctic Exploration . Born in Borge, Østfold , Norway, Amundsen began his career as a polar explorer as first mate on Adrien de Gerlache 's Belgian Antarctic Expedition of 1897–1899. From 1903 to 1906, he led the first expedition to successfully traverse the Northwest Passage on the sloop Gjøa . In 1909, Amundsen began planning for

9600-427: Was a biannual competition that ran from 2003 until 2011. It took place between the community of Resolute , on the shores of Resolute Bay , Nunavut , in northern Canada and the 1996 location of the north magnetic pole at 78°35′42″N 104°11′54″W  /  78.59500°N 104.19833°W  / 78.59500; -104.19833  ( Magnetic North Pole 1996 ) , also in northern Canada. On 25 July 2007,

9700-563: Was adapted into the TV serial The Last Place on Earth . It aired in 1985 and features Sverre Anker Ousdal as Amundsen. On 15 February 2019, a biographic Norwegian film titled Amundsen , directed by Espen Sandberg , was released. At least two Inuit in Gjøa Haven with European ancestry have claimed to be descendants of Amundsen, from the period of their extended winter stay on King William Island from 1903 to 1905. Accounts by members of

9800-527: Was called off in September 1928 by the Norwegian government, and the bodies were never found. In 2004 and in late August 2009, the Royal Norwegian Navy used the unmanned submarine Hugin 1000 to search for the wreckage of Amundsen's plane. The searches focused on a 40-square-mile (100 km ) area of the sea floor, and were documented by the German production company ContextTV. They found nothing from

9900-595: Was said to have ignored romantic relationships in pursuit of his goals. He "found little use in activities that didn't help him fulfill his polar ambitions". Owing to Amundsen's numerous significant accomplishments in polar exploration, many places in both the Arctic and Antarctic are named after him. The Amundsen–Scott South Pole Station , operated by the United States Antarctic Program , was jointly named in honour of Amundsen and his British rival Robert Falcon Scott . The Amundsen crater on

10000-568: Was to the northeasterly direction over the Kara Sea . Amundsen planned to freeze the Maud into the polar ice cap and drift towards the North Pole ;– as Nansen had done with the Fram  – and he did so off Cape Chelyuskin . But, the ice became so thick that the ship was unable to break free, although it was designed for such a journey in heavy ice. In September 1919,

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