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Related integral theorem. II. A method for obtaining quadratic constants of the motion for conservative dynamical systems admitting symmetries
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In this paper, it is shown that if a conservative dynamical system admits a trajectory collineation, then in general a new quadratic (in the velocity) constant of the motion will result from the deformation of a given quadratically constant of motion under such a symmetry mapping.Citations
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Dynamical symmetries and constants of the motion for classical particle systems
Gerald H. Katzin,Jack Levine +1 more
TL;DR: In this paper, the conditions for dynamical symmetry mappings directly at the level of the dynamical equations were derived and a generalized form of the related integral theorem (a method for obtaining constants of motion based upon deformations of a known constant of the motion under dynamical symmetries) was obtained.
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SL(3,R) as the group of symmetry transformations for all one‐dimensional linear systems
M. Aguirre,J. Krause +1 more
TL;DR: In this paper, the converse problem of similarity analysis is solved in general for the finite symmetry transformations of any inhomogeneous ordinary linear differential equation of the second order x+f2(t)x+f1(t),x =f0(t).
Journal ArticleDOI
Dynamical symmetries in mechanics
TL;DR: In this paper, the authors discuss methods that enable one to trace the origin of symmetry and conservation laws in mechanics to geometrical symmetries of space-time, which reveal their intimate relation to conservation laws.
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Infinitesimal symmetry transformations of some one-dimensional linear systems
M. Aguirre,J. Krause +1 more
TL;DR: In this article, the converse problem of similarity analysis is solved in general for the infinitesimal symmetry transformations of any given inhomogeneous ordinary differential equation of the second order x+f2(t)x+f1(t),x=f0(t).
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Integrating factors and conservation laws for nonconservative dynamical systems
Dj. S. Djukic,Tytti Sutela +1 more
TL;DR: In this paper, a general approach to the construction of conservation laws for classical non-conservative dynamical systems is presented, where conservation laws are constructed by finding corresponding integrating factors for the equations of motion.
References
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Book
Non-Riemannian geometry
TL;DR: Asymmetric connections Symmetric connections Projective geometry of paths The geometry of subspaces Bibliography as discussed by the authors, see Section 2.1 for a survey of the main sources.
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Existence of the Dynamic Symmetries O4 and SU3 for All Classical Central Potential Problems
TL;DR: In this article, it was shown that all non-relativistic central potential problems have both 0 4 and SU3 symmetries, and the internal invariances of these problems derive from a dynamical origin.
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Dynamical symmetries and constants of the motion for classical particle systems
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