Hojman method for solving differential equations

Abstract

First, the method presented by Hojman for finding the conserved quantity of the system of second order differential equations is generalized and applied to the system of first order differential equations, particularly to the odd-dimensional system for finding the integral in this paper. Next, it is proved that the Hojman theorem is a special case of the theorem given in this paper. Finally, an example is given to illustrate the application of the result.

Mei Symmetry and Conserved Quantity of Tzénoff Equations for Nonholonomic Systems of Non-Chetaev's Type

“…In what follows, let us prove it. Differentiating formula (27) In the same way, we have Proposition 5. Proposition 5 If the infinitesimal generators ξ k of the special Mei symmetry for the above system satisfy Eqs.…”

“…( 18), (19), and (25) and there exists a function µ = µ(t, q, q) to meet Eq. ( 26), then the strong Hojman conserved quantity in expression (27) is induced by the strong Mei symmetry.…”

Jacobi Last Multiplier Method for Equations of Motion of Constrained Mechanical Systems

“…The integral of differential equations of mechanical systems has important physical and mathematical meanings. The study of solving differential equations by using an analytical mechanics method includes a series of important contributions such as the analytical mechanics method [1] of solving first-order differential equations, the Hamilton-Jacobi method, [2] Birkhoff-Noether method, [3] Hojman method [4] of solving Emden-Fowler equations, [5] the method of solving Whittaker equations [6] and the three-particle Toda lattice problem, [7] etc. Jacobi introduced the concept of differential equation last multiplier in 1984.…”