![]() The Hamilton–Jacobi equations provide a commonly used and straightforward method for identifying constants of motion, particularly when the Hamiltonian adopts recognizable functional forms in orthogonal coordinates.The simplest but least systematic approach is the intuitive ("psychic") derivation, in which a quantity is hypothesized to be constant (perhaps because of experimental data) and later shown mathematically to be conserved throughout the motion.There are several methods for identifying constants of motion. Methods for identifying constants of motion ![]() ![]() Therefore, the identification of constants of motion is an important objective in mechanics. For example, Poinsot's construction shows that the torque-free rotation of a rigid body is the intersection of a sphere (conservation of total angular momentum) and an ellipsoid (conservation of energy), a trajectory that might be otherwise hard to derive and visualize. In fortunate cases, even the trajectory of the motion can be derived as the intersection of isosurfaces corresponding to the constants of motion. Common examples include energy, linear momentum, angular momentum and the Laplace–Runge–Lenz vector (for inverse-square force laws).Ĭonstants of motion are useful because they allow properties of the motion to be derived without solving the equations of motion. However, it is a mathematical constraint, the natural consequence of the equations of motion, rather than a physical constraint (which would require extra constraint forces). “ motion”, in Trésor de la langue française informatisé, 2012.įrom Old French motion, mocion, borrowed from Latin mōtio ( “ movement, motion ” ).In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion. ![]() ― It's all about a motion of no confidence. motion Il s’agit d’une motion de censure.Inherited from Old French motion, mocion, borrowed from Latin motiōnem, noun of action from perfect passive participle motus ( “ having been moved ” ), from verb movere ( “ move ” ), + noun of action suffix -io. exercise ( physical activity intended to improve strength and fitness ).Motion c ( singular definite motionen, not used in plural form) Vietnamese: cử động (vi) ( 舉動), vận động (vi) ( 運動)īorrowed from French motion, from Latin mōtio ( “ movement ” ), from movēre ( “ to move ” ).Estonian: liigutus (et), liikumine (et).( uncountable ) A state of progression from one place to another.Motion ( countable and uncountable, plural motions) ( General American ) IPA ( key): /ˈmoʊ.ʃən/.( Received Pronunciation ) IPA ( key): /ˈməʊ.ʃən/. ![]() From Middle English mocioun, mocion, from Anglo-Norman motion, Middle French motion, and their etymon Latin motio ( “ movement, motion ” ), related to movēre, from Proto-Indo-European *mew- ( “ to move ” ). ![]()
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