First integrals of motion in the deployment and retrieval of Shuttle-Tethered-Subsatellite system

1986 ◽  
Author(s):  
M. RAJAN ◽  
T. ANDERSON
Keyword(s):  
First Integrals ◽  
Integrals Of Motion ◽  
Tethered Subsatellite System

q-Equivalent Hamiltonian Operators

1972 ◽  
Vol 50 (17) ◽  
pp. 2037-2047 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit ◽  
First Integral ◽  
Canonical Commutation Relation ◽  
Equation Of Motion ◽  
First Integrals ◽  
Position Operator ◽  
Integrals Of Motion ◽  
Adjoint Operators ◽  
Hamiltonian Operators

From the equation of motion and the canonical commutation relation for the position of a particle and its conjugate momentum, different first integrals of motion can be constructed. In addition to the proper Hamiltonian, there are other operators that can be considered as the generators of motion for the position operator (q-equivalent Hamiltonians). All of these operators have the same classical limit for the probability density of the coordinate of the particle, and many of them are symmetric and self-adjoint operators or have self-adjoint extensions. However, they do not satisfy the Heisenberg rule of quantization, and lead to incorrect commutation relations for velocity and position operators. Therefore, it is concluded that the energy first integral and the potential, rather than the equation of motion and the force law, are the physically significant operators in quantum mechanics.

scholarly journals On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations

2005 ◽  
Vol 461 (2060) ◽  
pp. 2451-2477 ◽  
Author(s):  
V.K Chandrasekar ◽  
M Senthilvelan ◽  
M Lakshmanan
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Free Particle ◽  
First Integrals ◽  
Second Order ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Integrals Of Motion ◽  
Integrating Factors

A method for finding general solutions of second-order nonlinear ordinary differential equations by extending the Prelle–Singer (PS) method is briefly discussed. We explore integrating factors, integrals of motion and the general solution associated with several dynamical systems discussed in the current literature by employing our modifications and extensions of the PS method. We also introduce a novel way of deriving linearizing transformations from the first integrals to linearize the second-order nonlinear ordinary differential equations to free particle equations. We illustrate the theory with several potentially important examples and show that our procedure is widely applicable.

scholarly journals CLASSIFICATION OF YANG–MILLS FIELDS ADMITTING INTEGRALS OF MOTION FOR THE WONG EQUATIONS

2020 ◽  
pp. 14-24
Author(s):  
M. N. Boldyreva ◽  
A. A. Magazev ◽  
I. V. Shirokov
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
First Integrals ◽  
Gauge Fields ◽  
Dimensional Euclidean Space ◽  
Integrals Of Motion ◽  
Yang Mills ◽  
Linear Integral

In the paper, we investigate the gauge fields that are characterized by the existence of non-trivial integrals of motion for the Wong equations. For the gauge group 𝑆𝑈(2), the class of fields admitting only the isospin first integrals is described in detail. All gauge non-equivalent Yang–Mills fields admitting a linear integral of motion for the Wong equations are classified in the three-dimensional Euclidean space

Geodesic deviation and first integrals of motion

1982 ◽  
Vol 23 (12) ◽  
pp. 2346-2352 ◽  
Author(s):  
Giacomo Caviglia ◽  
Franco Salmistraro ◽  
Clara Zordan
Keyword(s):  
First Integrals ◽  
Integrals Of Motion ◽  
Geodesic Deviation

scholarly journals Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs

2018 ◽  
Vol 173 ◽  
pp. 01004 ◽  
Author(s):  
Victor Edneral
Keyword(s):  
Normal Form ◽  
Closed Form ◽  
Polynomial Systems ◽  
First Integrals ◽  
Degenerate System ◽  
Integrals Of Motion ◽  
Nonlinear Odes ◽  
Power Transformations ◽  
Normal Form Methods ◽  
Power Geometry

This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form. Example of creating exact first integrals of motion of some planar degenerate system in a closed form is given.

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