92-522: The Gymnotiformes / dʒ ɪ m ˈ n ɒ t ɪ f ɔːr m iː z / are an order of teleost bony fishes commonly known as Neotropical knifefish or South American knifefish . They have long bodies and swim using undulations of their elongated anal fin . Found almost exclusively in fresh water (the only exceptions are species that occasionally may visit brackish water to feed), these mostly nocturnal fish are capable of producing electric fields to detect prey , for navigation, communication, and, in
184-682: A circle instead of a line. The calculation takes every particle's x coordinate and maps it to an angle, θ i = x i x max 2 π {\displaystyle \theta _{i}={\frac {x_{i}}{x_{\max }}}2\pi } where x max is the system size in the x direction and x i ∈ [ 0 , x max ) {\displaystyle x_{i}\in [0,x_{\max })} . From this angle, two new points ( ξ i , ζ i ) {\displaystyle (\xi _{i},\zeta _{i})} can be generated, which can be weighted by
276-420: A movable premaxilla and corresponding modifications in the jaw musculature which make it possible for them to protrude their jaws outwards from the mouth . This is of great advantage, enabling them to grab prey and draw it into the mouth . In more derived teleosts, the enlarged premaxilla is the main tooth-bearing bone, and the maxilla, which is attached to the lower jaw, acts as a lever, pushing and pulling
368-799: A muscle that allows the pharyngeal jaws to have a role in grinding food in addition to transporting it. The caudal fin is homocercal , meaning the upper and lower lobes are about equal in size. The spine ends at the caudal peduncle, the base of the caudal fin, distinguishing this group from those in which the spine extends into the upper lobe of the caudal fin, such as most fish from the Paleozoic (541 to 252 million years ago). The neural arches are elongated to form uroneurals which provide support for this upper lobe. Teleosts tend to be quicker and more flexible than more basal bony fishes. Their skeletal structure has evolved towards greater lightness. While teleost bones are well calcified , they are constructed from
460-454: A nest and fanning the eggs to keep them well-oxygenated. Teleosts are economically important to humans, as is shown by their depiction in art over the centuries. The fishing industry harvests them for food, and anglers attempt to capture them for sport . Some species are farmed commercially, and this method of production is likely to be increasingly important in the future. Others are kept in aquariums or used in research, especially in
552-783: A red lightning flash [REDACTED] . There are other electric fishes in other families (not shown). Siluriformes (catfish) ( some [REDACTED] [REDACTED] ) [REDACTED] Apteronotidae (ghost knifefishes) [REDACTED] [REDACTED] Hypopomidae (bluntnose knifefishes) [REDACTED] [REDACTED] Rhamphichthyidae (sand knifefishes) [REDACTED] [REDACTED] Gymnotus (banded knifefishes) [REDACTED] [REDACTED] Electrophorus (electric eels) [REDACTED] [REDACTED] [REDACTED] Sternopygidae (glass knifefishes) [REDACTED] [REDACTED] Characoidei ( piranhas , tetras , and allies) [REDACTED] Gymnotiform fishes inhabit freshwater rivers and streams throughout
644-401: A scaffolding of struts, rather than the dense cancellous bones of holostean fish. In addition, the lower jaw of the teleost is reduced to just three bones; the dentary , the angular bone and the articular bone . The genital and urinary tracts end behind the anus in the genital papilla ; this is observed to sex teleosts. The teleosts were first recognised as a distinct group by
736-413: Is a particle with its mass concentrated at the center of mass. By selecting the center of gravity as the reference point for a rigid body, the gravity forces will not cause the body to rotate, which means the weight of the body can be considered to be concentrated at the center of mass. The linear and angular momentum of a collection of particles can be simplified by measuring the position and velocity of
828-534: Is also a factor contributing to the diversity of electric signals observed in Gymnotiformes. Reduced gene flow due to geographical barriers has led to vast differences signal morphology in different streams and drainages. Teleost See text Teleostei ( / ˌ t ɛ l i ˈ ɒ s t i aɪ / ; Greek teleios "complete" + osteon "bone"), members of which are known as teleosts ( / ˈ t ɛ l i ɒ s t s , ˈ t iː l i -/ ), is, by far,
920-422: Is always directly below the rotorhead . In forward flight, the center of mass will move forward to balance the negative pitch torque produced by applying cyclic control to propel the helicopter forward; consequently a cruising helicopter flies "nose-down" in level flight. The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the barycenter . The barycenter
1012-668: Is chosen as the center of mass these equations simplify to p = m v , L = ∑ i = 1 n m i ( r i − R ) × d d t ( r i − R ) + ∑ i = 1 n m i R × v {\displaystyle \mathbf {p} =m\mathbf {v} ,\quad \mathbf {L} =\sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )\times {\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+\sum _{i=1}^{n}m_{i}\mathbf {R} \times \mathbf {v} } where m
SECTION 10
#17327823464731104-439: Is covered by a toothplate. The fourth arch is composed of pairs of ceratobranchials and epibranchials, and sometimes additionally, some pharyngobranchials and a basibranchial. The base of the lower pharyngeal jaws is formed by the fifth ceratobranchials while the second, third and fourth pharyngobranchials create the base of the upper. In the more basal teleosts the pharyngeal jaws consist of well-separated thin parts that attach to
1196-468: Is crucial, possibly resulting in severe injury or death if assumed incorrectly. A center of gravity that is at or above the lift point will most likely result in a tip-over incident. In general, the further the center of gravity below the pick point, the safer the lift. There are other things to consider, such as shifting loads, strength of the load and mass, distance between pick points, and number of pick points. Specifically, when selecting lift points, it
1288-406: Is determined exclusively by the ribbon fins and the contribution of the pectoral fins for forward movement was negligible. The body is kept relatively rigid and there is very little motion of the center of mass motion during locomotion compared to the body size of the fish. The caudal fin is absent, or in the apteronotids, greatly reduced. The gill opening is restricted. The anal opening is under
1380-411: Is generated day and night throughout the entire life of the individual. Certain aspects of the electric signal are unique to each species, especially a combination of the pulse waveform, duration, amplitude, phase and frequency. The electric organs of most Gymnotiformes produce tiny discharges of just a few millivolts , far too weak to cause any harm to other fish. Instead, they are used to help navigate
1472-432: Is something of a colloquialism, but it is in common usage and when gravity gradient effects are negligible, center-of-gravity and mass-center are the same and are used interchangeably. In physics the benefits of using the center of mass to model a mass distribution can be seen by considering the resultant of the gravity forces on a continuous body. Consider a body Q of volume V with density ρ ( r ) at each point r in
1564-1708: Is the mass at the point r , g is the acceleration of gravity, and k ^ {\textstyle \mathbf {\hat {k}} } is a unit vector defining the vertical direction. Choose a reference point R in the volume and compute the resultant force and torque at this point, F = ∭ Q f ( r ) d V = ∭ Q ρ ( r ) d V ( − g k ^ ) = − M g k ^ , {\displaystyle \mathbf {F} =\iiint _{Q}\mathbf {f} (\mathbf {r} )\,dV=\iiint _{Q}\rho (\mathbf {r} )\,dV\left(-g\mathbf {\hat {k}} \right)=-Mg\mathbf {\hat {k}} ,} and T = ∭ Q ( r − R ) × f ( r ) d V = ∭ Q ( r − R ) × ( − g ρ ( r ) d V k ^ ) = ( ∭ Q ρ ( r ) ( r − R ) d V ) × ( − g k ^ ) . {\displaystyle \mathbf {T} =\iiint _{Q}(\mathbf {r} -\mathbf {R} )\times \mathbf {f} (\mathbf {r} )\,dV=\iiint _{Q}(\mathbf {r} -\mathbf {R} )\times \left(-g\rho (\mathbf {r} )\,dV\,\mathbf {\hat {k}} \right)=\left(\iiint _{Q}\rho (\mathbf {r} )\left(\mathbf {r} -\mathbf {R} \right)dV\right)\times \left(-g\mathbf {\hat {k}} \right).} If
1656-511: Is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet , or a planet orbits a star , both bodies are actually orbiting a point that lies away from the center of the primary (larger) body. For example, the Moon does not orbit the exact center of the Earth , but a point on a line between
1748-903: Is the sum of the masses of all of the particles. These values are mapped back into a new angle, θ ¯ {\displaystyle {\overline {\theta }}} , from which the x coordinate of the center of mass can be obtained: θ ¯ = atan2 ( − ζ ¯ , − ξ ¯ ) + π x com = x max θ ¯ 2 π {\displaystyle {\begin{aligned}{\overline {\theta }}&=\operatorname {atan2} \left(-{\overline {\zeta }},-{\overline {\xi }}\right)+\pi \\x_{\text{com}}&=x_{\max }{\frac {\overline {\theta }}{2\pi }}\end{aligned}}} The process can be repeated for all dimensions of
1840-474: Is the total mass of all the particles, p is the linear momentum, and L is the angular momentum. The law of conservation of momentum predicts that for any system not subjected to external forces the momentum of the system will remain constant, which means the center of mass will move with constant velocity. This applies for all systems with classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More formally, this
1932-1282: Is the unit vector in the vertical direction). Let r 1 , r 2 , and r 3 be the position coordinates of the support points, then the coordinates R of the center of mass satisfy the condition that the resultant torque is zero, T = ( r 1 − R ) × F 1 + ( r 2 − R ) × F 2 + ( r 3 − R ) × F 3 = 0 , {\displaystyle \mathbf {T} =(\mathbf {r} _{1}-\mathbf {R} )\times \mathbf {F} _{1}+(\mathbf {r} _{2}-\mathbf {R} )\times \mathbf {F} _{2}+(\mathbf {r} _{3}-\mathbf {R} )\times \mathbf {F} _{3}=0,} or R × ( − W k ^ ) = r 1 × F 1 + r 2 × F 2 + r 3 × F 3 . {\displaystyle \mathbf {R} \times \left(-W\mathbf {\hat {k}} \right)=\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\mathbf {r} _{3}\times \mathbf {F} _{3}.} This equation yields
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#17327823464732024-434: Is true for any internal forces that cancel in accordance with Newton's Third Law . The experimental determination of a body's center of mass makes use of gravity forces on the body and is based on the fact that the center of mass is the same as the center of gravity in the parallel gravity field near the earth's surface. The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus,
2116-418: Is undefined. This is a correct result, because it only occurs when all particles are exactly evenly spaced. In that condition, their x coordinates are mathematically identical in a periodic system . A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes. Where a gravity field can be considered to be uniform, the mass-center and the center-of-gravity will be
2208-416: Is very important to place the center of gravity at the center and well below the lift points. The center of mass of the adult human body is 10 cm above the trochanter (the femur joins the hip). In kinesiology and biomechanics, the center of mass is an important parameter that assists people in understanding their human locomotion. Typically, a human's center of mass is detected with one of two methods:
2300-1141: The ( ξ , ζ ) {\displaystyle (\xi ,\zeta )} plane, these coordinates lie on a circle of radius 1. From the collection of ξ i {\displaystyle \xi _{i}} and ζ i {\displaystyle \zeta _{i}} values from all the particles, the averages ξ ¯ {\displaystyle {\overline {\xi }}} and ζ ¯ {\displaystyle {\overline {\zeta }}} are calculated. ξ ¯ = 1 M ∑ i = 1 n m i ξ i , ζ ¯ = 1 M ∑ i = 1 n m i ζ i , {\displaystyle {\begin{aligned}{\overline {\xi }}&={\frac {1}{M}}\sum _{i=1}^{n}m_{i}\xi _{i},\\{\overline {\zeta }}&={\frac {1}{M}}\sum _{i=1}^{n}m_{i}\zeta _{i},\end{aligned}}} where M
2392-655: The Anguilliformes , the true eels. Their relationships were analysed by sequencing their mitochondrial genomes in 2019. This shows that contrary to earlier ideas, the Apteronotidae and Sternopygidae are not sister taxa , and that the Gymnotidae are deeply nested among the other families. Actively electrolocating fish are marked on the phylogenetic tree with a small yellow lightning flash [REDACTED] . Fish able to deliver electric shocks are marked with
2484-539: The Triassic period ( Prohalecites , Pholidophorus ). However, it has been suggested that teleosts probably first evolved already during the Paleozoic era . During the Mesozoic and Cenozoic eras they diversified widely, and as a result, 96% of all living fish species are teleosts. The cladogram below shows the evolutionary relationships of the teleosts to other extant clades of bony fish, and to
2576-488: The center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point ) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration . Calculations in mechanics are often simplified when formulated with respect to
2668-544: The centroid . The center of mass may be located outside the physical body , as is sometimes the case for hollow or open-shaped objects, such as a horseshoe . In the case of a distribution of separate bodies, such as the planets of the Solar System , the center of mass may not correspond to the position of any individual member of the system. The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as
2760-451: The linear and angular momentum of planetary bodies and rigid body dynamics . In orbital mechanics , the equations of motion of planets are formulated as point masses located at the centers of mass (see Barycenter (astronomy) for details). The center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system . The concept of center of gravity or weight
2852-440: The percentage of the total mass divided between these two particles vary from 100% P 1 and 0% P 2 through 50% P 1 and 50% P 2 to 0% P 1 and 100% P 2 , then the center of mass R moves along the line from P 1 to P 2 . The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, and are termed barycentric coordinates . Another way of interpreting
Gymnotiformes - Misplaced Pages Continue
2944-541: The German ichthyologist Johannes Peter Müller in 1845. The name is from Greek teleios , "complete" + osteon , "bone". Müller based this classification on certain soft tissue characteristics, which would prove to be problematic, as it did not take into account the distinguishing features of fossil teleosts. In 1966, Greenwood et al. provided a more solid classification. The oldest fossils of teleosteomorphs (the stem group from which teleosts later evolved) date back to
3036-516: The amplitude of its undulations, however it was directly related to the frequency of the waves generated. Studies have shown that the natural angle between the body of the knifefish and its fin is essential for efficient forward motion, for if the anal fin was located directly underneath, then an upwards force would be generated with forward thrust, which would require an additional downwards force in order to maintain neutral buoyancy . A combination of forward and reverse wave patterns, which meet towards
3128-698: The ancestor to modern-day Gymnotiformes and Siluriformes were estimated to have convergently evolved ampullary receptors, allowing for passive electroreceptive capabilities. As this characteristic occurred after the prior loss of electroreception among the subclass Neopterygii after having been present in the common ancestor of vertebrates, the ampullary receptors of Gymnotiformes are not homologous with those of other jawed non-teleost species, such as chondricthyans. Gymnotiformes and Mormyridae have developed their electric organs and electrosensory systems (ESSs) through convergent evolution . As Arnegard et al. (2005) and Albert and Crampton (2005) show, their last common ancestor
3220-500: The case of a system of particles P i , i = 1, ..., n , each with mass m i that are located in space with coordinates r i , i = 1, ..., n , the coordinates R of the center of mass satisfy ∑ i = 1 n m i ( r i − R ) = 0 . {\displaystyle \sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )=\mathbf {0} .} Solving this equation for R yields
3312-428: The case of the electric eel ( Electrophorus electricus ), attack and defense. A few species are familiar to the aquarium trade , such as the black ghost knifefish ( Apteronotus albifrons ), the glass knifefish ( Eigenmannia virescens ), and the banded knifefish ( Gymnotus carapo ). Aside from the electric eel ( Electrophorus electricus ), Gymnotiformes are slender fish with narrow bodies and tapering tails, hence
3404-488: The center of mass is the same as the centroid of the volume. The coordinates R of the center of mass of a two-particle system, P 1 and P 2 , with masses m 1 and m 2 is given by R = m 1 r 1 + m 2 r 2 m 1 + m 2 . {\displaystyle \mathbf {R} ={{m_{1}\mathbf {r} _{1}+m_{2}\mathbf {r} _{2}} \over m_{1}+m_{2}}.} Let
3496-406: The center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere. In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry. An experimental method for locating the center of mass is to suspend
3588-493: The center of mass of the whole is the weighted average of the centers. This method can even work for objects with holes, which can be accounted for as negative masses. A direct development of the planimeter known as an integraph, or integerometer, can be used to establish the position of the centroid or center of mass of an irregular two-dimensional shape. This method can be applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult. It
3680-421: The center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion . In the case of a single rigid body , the center of mass is fixed in relation to the body, and if the body has uniform density , it will be located at
3772-509: The center of the Earth and the Moon, approximately 1,710 km (1,062 miles) below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun . If the masses are more similar, e.g., Pluto and Charon , the barycenter will fall outside both bodies. Knowing the location of the center of gravity when rigging
Gymnotiformes - Misplaced Pages Continue
3864-437: The center of the anal fin, produce a heave force allowing for hovering, or upwards movement. The ghost knifefish can vary the undulation of the waves, as well as the angle of attack of the fin to achieve various directional changes. The pectoral fins of these fishes can help to control roll and pitch control. By rolling they can generate a vertical thrust to quickly, and efficiently, ambush their prey. The forward movement
3956-484: The common name of "knifefishes". They have neither pelvic fins nor dorsal fins , but do possess greatly elongated anal fins that stretch along almost the entire underside of their bodies. The fish swim by rippling this fin, keeping their bodies rigid. This means of propulsion allows them to move backwards as easily as they move forward. The knifefish has approximately one hundred and fifty fin rays along its ribbon-fin. These individual fin rays can be curved nearly twice
4048-464: The concept further. Newton's second law is reformulated with respect to the center of mass in Euler's first law . The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space. In
4140-399: The coordinates R to obtain R = 1 M ∭ Q ρ ( r ) r d V , {\displaystyle \mathbf {R} ={\frac {1}{M}}\iiint _{Q}\rho (\mathbf {r} )\mathbf {r} \,dV,} Where M is the total mass in the volume. If a continuous mass distribution has uniform density , which means that ρ is constant, then
4232-623: The coordinates of the center of mass R * in the horizontal plane as, R ∗ = − 1 W k ^ × ( r 1 × F 1 + r 2 × F 2 + r 3 × F 3 ) . {\displaystyle \mathbf {R} ^{*}=-{\frac {1}{W}}\mathbf {\hat {k}} \times (\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}+\mathbf {r} _{3}\times \mathbf {F} _{3}).} The center of mass lies on
4324-631: The direction of the current through the electrocytes in the electric organ), the amplitude of the wave, the frequency of the wave, and the number of phases of the wave. One significant force driving this evolution is predation. The most common predators of Gymnotiformes include the closely related Siluriformes (catfish), as well as predation within families ( E. electricus is one of the largest predators of Gymnotus ). These predators sense electric fields, but only at low frequencies, thus certain species of Gymnotiformes, such as those in Gymnotus , have shifted
4416-436: The distinction between the center-of-gravity and the mass-center. Any horizontal offset between the two will result in an applied torque. The mass-center is a fixed property for a given rigid body (e.g. with no slosh or articulation), whereas the center-of-gravity may, in addition, depend upon its orientation in a non-uniform gravitational field. In the latter case, the center-of-gravity will always be located somewhat closer to
4508-485: The environment, including locating the bottom-dwelling invertebrates that compose their diets. They may also be used to send signals between fish of the same species. In addition to this low-level field, the electric eel also has the capability to produce much more powerful discharges to stun prey. There are currently about 250 valid gymnotiform species in 34 genera and five families, with many additional species yet to be formally described . The actual number of species in
4600-414: The female lays a batch of eggs, the male fertilises them and the larvae develop without any further parental involvement. A fair proportion of teleosts are sequential hermaphrodites , starting life as females and transitioning to males at some stage, with a few species reversing this process. A small percentage of teleosts are viviparous and some provide parental care with typically the male fish guarding
4692-410: The fields of genetics and developmental biology . Distinguishing features of the teleosts are mobile premaxilla , elongated neural arches at the end of the caudal fin and unpaired basibranchial toothplates. The premaxilla is unattached to the neurocranium (braincase); it plays a role in protruding the mouth and creating a circular opening. This lowers the pressure inside the mouth, sucking
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#17327823464734784-453: The fin resembles traveling sinusoidal waves . A forward traveling wave can be associated with forward motion, while a wave in the reverse direction produces thrust in the opposite direction. This undulating motion of the fin produced a system of linked vortex tubes that were produced along the bottom edge of the fin. A jet was produced at an angle to the fin that was directly related to the vortex tubes, and this jet provides propulsion that moves
4876-424: The fish forward. The wave motion of the fin is similar to that of other marine creatures, such as the undulation of the body of an eel , however the wake vortex produced by the knifefish was found to be a reverse Kármán vortex . This type of vortex is also produced by some fish, such as trout , through the oscillations of their caudal fins . The speed at which the fish moved through the water had no correlation to
4968-405: The formula R = ∑ i = 1 n m i r i ∑ i = 1 n m i . {\displaystyle \mathbf {R} ={\sum _{i=1}^{n}m_{i}\mathbf {r} _{i} \over \sum _{i=1}^{n}m_{i}}.} If the mass distribution is continuous with the density ρ( r ) within a solid Q , then
5060-721: The four-limbed vertebrates ( tetrapods ) that evolved from a related group of bony fish during the Devonian period . Approximate divergence dates (in millions of years, mya ) are from Near et al., 2012. Coelacanths [REDACTED] Lungfish [REDACTED] Lissamphibia [REDACTED] Mammals [REDACTED] Sauropsida ( reptiles , birds ) [REDACTED] Polypteriformes ( bichirs , reedfishes ) [REDACTED] Acipenseriformes ( sturgeons , paddlefishes ) [REDACTED] Lepisosteiformes ( gars ) [REDACTED] Amiiformes ( bowfin ) [REDACTED] Teleostei [REDACTED] The phylogeny of
5152-407: The frequency of their signals so they can be effectively invisible. Sexual selection is another driving force with an unusual influence, in that females exhibit preference for males with low-frequency signals (which are more easily detected by predators), but most males exhibit this frequency only intermittently. Females prefer males with low-frequency signals because they indicate a higher fitness of
5244-420: The head or the pectoral fins. These fish possess electric organs that allow them to produce electric fields, which are usually weak. In most gymnotiforms, the electric organs are derived from muscle cells. However, adult apteronotids are one exception, as theirs are derived from nerve cells (spinal electromotor neurons). In gymnotiforms, the electric organ discharge may be continuous or pulsed. If continuous, it
5336-660: The humid Neotropics , ranging from southern Mexico to northern Argentina . They are nocturnal fishes. The families Gymnotidae and Hypopomidae are most diverse (numbers of species) and abundant ( numbers of individuals ) in small non-floodplain streams and rivers, and in floodplain "floating meadows" of aquatic macrophytes (e.g., Eichornium , the Amazonian water hyacinth ). On the other hand, families Apteronotidae and Sternopygidae are most diverse and abundant in large rivers. Species of Rhamphichthyidae are moderately diverse in all these habitat types. Gymnotiformes are among
5428-439: The integral of the weighted position coordinates of the points in this volume relative to the center of mass R over the volume V is zero, that is ∭ Q ρ ( r ) ( r − R ) d V = 0 . {\displaystyle \iiint _{Q}\rho (\mathbf {r} )\left(\mathbf {r} -\mathbf {R} \right)dV=\mathbf {0} .} Solve this equation for
5520-786: The largest infraclass in the class Actinopterygii , the ray-finned fishes, and contains 96% of all extant species of fish . Teleosts are arranged into about 40 orders and 448 families . Over 26,000 species have been described. Teleosts range from giant oarfish measuring 7.6 m (25 ft) or more, and ocean sunfish weighing over 2 t (2.0 long tons; 2.2 short tons), to the minute male anglerfish Photocorynus spiniceps , just 6.2 mm (0.24 in) long. Including not only torpedo-shaped fish built for speed, teleosts can be flattened vertically or horizontally, be elongated cylinders or take specialised shapes as in anglerfish and seahorses . The difference between teleosts and other bony fish lies mainly in their jaw bones; teleosts have
5612-404: The main attractive body as compared to the mass-center, and thus will change its position in the body of interest as its orientation is changed. In the study of the dynamics of aircraft, vehicles and vessels, forces and moments need to be resolved relative to the mass center. That is true independent of whether gravity itself is a consideration. Referring to the mass-center as the center-of-gravity
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#17327823464735704-627: The male. Since these low-frequency signals are more conspicuous to predators, the emitting of such signals by males shows that they are capable of evading predation. Therefore, the production of low-frequency signals is under competing evolutionary forces: it is selected against due to the eavesdropping of electric predators, but is favored by sexual selection due to its attractiveness to females. Females also prefer males with longer pulses, also energetically expensive, and large tail lengths. These signs indicate some ability to exploit resources, thus indicating better lifetime reproductive success. Genetic drift
5796-512: The mass of the particle x i {\displaystyle x_{i}} for the center of mass or given a value of 1 for the geometric center: ξ i = cos ( θ i ) ζ i = sin ( θ i ) {\displaystyle {\begin{aligned}\xi _{i}&=\cos(\theta _{i})\\\zeta _{i}&=\sin(\theta _{i})\end{aligned}}} In
5888-428: The maximum recorded curvature for ray-finned fish fin rays during locomotion . These fin rays are curved into the direction of motion, indicating that the knifefish has active control of the fin ray curvature, and that this curvature is not the result of passive bending due to fluid loading. Different wave patterns produced along the length of the elongated anal fin allow for various forms of thrust. The wave motion of
5980-569: The more derived members of Ostariophysi , a lineage of primary freshwater fishes. The only known fossils are from the Miocene about 7 million years ago ( Mya ) of Bolivia . Gymnotiformes has no extant species in Africa . This may be because they did not spread into Africa before South America and Africa split, or it may be that they were out-competed by Mormyridae , which are similar in that they also use electrolocation . Approximately 150 Mya,
6072-406: The neurocranium, pectoral girdle , and hyoid bar . Their function is limited to merely transporting food, and they rely mostly on lower pharyngeal jaw activity. In more derived teleosts the jaws are more powerful, with left and right ceratobranchials fusing to become one lower jaw; the pharyngobranchials fuse to create a large upper jaw that articulates with the neurocranium. They have also developed
6164-471: The nodes (so, the pattern of branching shown is likely to be correct). They calibrated (set actual values for) branching times in this tree from 36 reliable measurements of absolute time from the fossil record. The teleosts are divided into the major clades shown on the cladogram, with dates, following Near et al. More recent research divide the teleosts into two major groups: Eloposteoglossocephala (Elopomorpha + Osteoglossomorpha) and Clupeocephala (the rest of
6256-463: The object from two locations and to drop plumb lines from the suspension points. The intersection of the two lines is the center of mass. The shape of an object might already be mathematically determined, but it may be too complex to use a known formula. In this case, one can subdivide the complex shape into simpler, more elementary shapes, whose centers of mass are easy to find. If the total mass and center of mass can be determined for each area, then
6348-520: The object. The center of mass will be the intersection of the two lines L 1 and L 2 obtained from the two experiments. Engineers try to design a sports car so that its center of mass is lowered to make the car handle better, which is to say, maintain traction while executing relatively sharp turns. The characteristic low profile of the U.S. military Humvee was designed in part to allow it to tilt farther than taller vehicles without rolling over , by ensuring its low center of mass stays over
6440-741: The particles relative to the center of mass. Let the system of particles P i , i = 1, ..., n of masses m i be located at the coordinates r i with velocities v i . Select a reference point R and compute the relative position and velocity vectors, r i = ( r i − R ) + R , v i = d d t ( r i − R ) + v . {\displaystyle \mathbf {r} _{i}=(\mathbf {r} _{i}-\mathbf {R} )+\mathbf {R} ,\quad \mathbf {v} _{i}={\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+\mathbf {v} .} The total linear momentum and angular momentum of
6532-415: The point of being unable to rotate for takeoff or flare for landing. If the center of mass is behind the aft limit, the aircraft will be more maneuverable, but also less stable, and possibly unstable enough so as to be impossible to fly. The moment arm of the elevator will also be reduced, which makes it more difficult to recover from a stalled condition. For helicopters in hover , the center of mass
6624-469: The premaxilla as the mouth is opened and closed. Other bones further back in the mouth serve to grind and swallow food. Another difference is that the upper and lower lobes of the tail (caudal) fin are about equal in size. The spine ends at the caudal peduncle , distinguishing this group from other fish in which the spine extends into the upper lobe of the tail fin. Teleosts have adopted a range of reproductive strategies . Most use external fertilisation:
6716-436: The prey inside. The lower jaw and maxilla are then pulled back to close the mouth, and the fish is able to grasp the prey . By contrast, mere closure of the jaws would risk pushing food out of the mouth. In more advanced teleosts, the premaxilla is enlarged and has teeth, while the maxilla is toothless. The maxilla functions to push both the premaxilla and the lower jaw forward. To open the mouth, an adductor muscle pulls back
6808-461: The process here is the mechanical balancing of moments about an arbitrary point. The numerator gives the total moment that is then balanced by an equivalent total force at the center of mass. This can be generalized to three points and four points to define projective coordinates in the plane, and in space, respectively. For particles in a system with periodic boundary conditions two particles can be neighbours even though they are on opposite sides of
6900-431: The reaction board method is a static analysis that involves the person lying down on that instrument, and use of their static equilibrium equation to find their center of mass; the segmentation method relies on a mathematical solution based on the physical principle that the summation of the torques of individual body sections, relative to a specified axis , must equal the torque of the whole system that constitutes
6992-429: The reference point R is chosen so that it is the center of mass, then ∭ Q ρ ( r ) ( r − R ) d V = 0 , {\displaystyle \iiint _{Q}\rho (\mathbf {r} )\left(\mathbf {r} -\mathbf {R} \right)dV=0,} which means the resultant torque T = 0 . Because the resultant torque is zero the body will move as though it
7084-401: The same. However, for satellites in orbit around a planet, in the absence of other torques being applied to a satellite, the slight variation (gradient) in gravitational field between closer-to and further-from the planet (stronger and weaker gravity respectively) can lead to a torque that will tend to align the satellite such that its long axis is vertical. In such a case, it is important to make
7176-418: The space bounded by the four wheels even at angles far from the horizontal . The center of mass is an important point on an aircraft , which significantly affects the stability of the aircraft. To ensure the aircraft is stable enough to be safe to fly, the center of mass must fall within specified limits. If the center of mass is ahead of the forward limit , the aircraft will be less maneuverable, possibly to
7268-1500: The system are p = d d t ( ∑ i = 1 n m i ( r i − R ) ) + ( ∑ i = 1 n m i ) v , {\displaystyle \mathbf {p} ={\frac {d}{dt}}\left(\sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )\right)+\left(\sum _{i=1}^{n}m_{i}\right)\mathbf {v} ,} and L = ∑ i = 1 n m i ( r i − R ) × d d t ( r i − R ) + ( ∑ i = 1 n m i ) [ R × d d t ( r i − R ) + ( r i − R ) × v ] + ( ∑ i = 1 n m i ) R × v {\displaystyle \mathbf {L} =\sum _{i=1}^{n}m_{i}(\mathbf {r} _{i}-\mathbf {R} )\times {\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+\left(\sum _{i=1}^{n}m_{i}\right)\left[\mathbf {R} \times {\frac {d}{dt}}(\mathbf {r} _{i}-\mathbf {R} )+(\mathbf {r} _{i}-\mathbf {R} )\times \mathbf {v} \right]+\left(\sum _{i=1}^{n}m_{i}\right)\mathbf {R} \times \mathbf {v} } If R
7360-615: The system to determine the complete center of mass. The utility of the algorithm is that it allows the mathematics to determine where the "best" center of mass is, instead of guessing or using cluster analysis to "unfold" a cluster straddling the periodic boundaries. If both average values are zero, ( ξ ¯ , ζ ¯ ) = ( 0 , 0 ) {\displaystyle \left({\overline {\xi }},{\overline {\zeta }}\right)=(0,0)} , then θ ¯ {\displaystyle {\overline {\theta }}}
7452-440: The system. This occurs often in molecular dynamics simulations, for example, in which clusters form at random locations and sometimes neighbouring atoms cross the periodic boundary. When a cluster straddles the periodic boundary, a naive calculation of the center of mass will be incorrect. A generalized method for calculating the center of mass for periodic systems is to treat each coordinate, x and y and/or z , as if it were on
7544-471: The teleosts has been subject to long debate, without consensus on either their phylogeny or the timing of the emergence of the major groups before the application of modern DNA -based cladistic analysis. Near et al. (2012) explored the phylogeny and divergence times of every major lineage, analysing the DNA sequences of 9 unlinked genes in 232 species. They obtained well-resolved phylogenies with strong support for
7636-1506: The teleosts). Hiodontiformes ( mooneyes ) [REDACTED] Osteoglossiformes ( bonytongues , elephantfishes ) [REDACTED] Elopiformes ( tenpounders , tarpons ) [REDACTED] Albuliformes ( Japanese gissus and bonefishes ) [REDACTED] Notacanthiformes (deep sea spiny eels) [REDACTED] Anguilliformes (true eels ) [REDACTED] Clupeiformes ( herrings ) [REDACTED] Alepocephaliformes ( slickheads ) [REDACTED] Gonorynchiformes ( milkfish ) [REDACTED] Cypriniformes ( minnows , carps , loaches ) [REDACTED] Characiformes ( tetras , piranhas ) [REDACTED] Gymnotiformes (knifefish and electric eels ) [REDACTED] Siluriformes (catfish) [REDACTED] Lepidogalaxiiformes (salamanderfish) Argentiniformes (marine smelts) [REDACTED] Galaxiiformes ( whitebait , mudfishes) [REDACTED] Esociformes ( pike ) [REDACTED] Salmoniformes ( salmon , trout ) [REDACTED] Stomiiformes (dragonfish) [REDACTED] Osmeriformes ( smelt ) [REDACTED] Ateleopodiformes (jellynoses) [REDACTED] Aulopiformes (lizardfish) [REDACTED] Myctophiformes ( lanternfish ) [REDACTED] Lampriformes ( oarfish , opah , ribbonfish ) [REDACTED] Percopsiformes (troutperches) [REDACTED] Zeiformes (dories) [REDACTED] Stylephoriformes (tube-eyes/thread-fins) Center of mass In physics ,
7728-477: The theory of the center of mass include Hero of Alexandria and Pappus of Alexandria . In the Renaissance and Early Modern periods, work by Guido Ubaldi , Francesco Maurolico , Federico Commandino , Evangelista Torricelli , Simon Stevin , Luca Valerio , Jean-Charles de la Faille , Paul Guldin , John Wallis , Christiaan Huygens , Louis Carré , Pierre Varignon , and Alexis Clairaut expanded
7820-509: The top of the maxilla, pushing the lower jaw forward. In addition, the maxilla rotates slightly, which pushes forward a bony process that interlocks with the premaxilla. The pharyngeal jaws of teleosts, a second set of jaws contained within the throat, are composed of five branchial arches , loops of bone which support the gills . The first three arches include a single basibranchial surrounded by two hypobranchials, ceratobranchials, epibranchials and pharyngobranchials. The median basibranchial
7912-442: The vertical line L , given by L ( t ) = R ∗ + t k ^ . {\displaystyle \mathbf {L} (t)=\mathbf {R} ^{*}+t\mathbf {\hat {k}} .} The three-dimensional coordinates of the center of mass are determined by performing this experiment twice with the object positioned so that these forces are measured for two different horizontal planes through
8004-430: The volume. In a parallel gravity field the force f at each point r is given by, f ( r ) = − d m g k ^ = − ρ ( r ) d V g k ^ , {\displaystyle \mathbf {f} (\mathbf {r} )=-dm\,g\mathbf {\hat {k}} =-\rho (\mathbf {r} )\,dV\,g\mathbf {\hat {k}} ,} where dm
8096-407: The weights were moved to a single point—their center of mass. In his work On Floating Bodies , Archimedes demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. Other ancient mathematicians who contributed to
8188-609: The wild is unknown. Gymnotiformes is thought to be the sister group to the Siluriformes from which they diverged in the Cretaceous period (about 120 million years ago). The families have traditionally been classified over suborders and superfamilies as below. Order Gymnotiformes Most gymnotiforms are weakly electric, capable of active electrolocation but not of delivering shocks. The electric eels, genus Electrophorus , are strongly electric, and are not closely related to
8280-604: Was regularly used by ship builders to compare with the required displacement and center of buoyancy of a ship, and ensure it would not capsize. An experimental method to locate the three-dimensional coordinates of the center of mass begins by supporting the object at three points and measuring the forces, F 1 , F 2 , and F 3 that resist the weight of the object, W = − W k ^ {\displaystyle \mathbf {W} =-W\mathbf {\hat {k}} } ( k ^ {\displaystyle \mathbf {\hat {k}} }
8372-433: Was roughly 140 to 208 Mya, and at this time they did not possess ESSs. Each species of Mormyrus (family: Mormyridae) and Gymnotus (family: Gymnotidae) have evolved a unique waveform that allows the individual fish to identify between species, genders, individuals and even between mates with better fitness levels. The differences include the direction of the initial phase of the wave (positive or negative, which correlates to
8464-436: Was studied extensively by the ancient Greek mathematician , physicist , and engineer Archimedes of Syracuse . He worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of
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