In this paper,we studied the canonical transformations of second-order non-standard general-ized mechanics with exponential Lagrangians and Poisson theory on the first integrals.First,Hamilton principle of second-order nonstandard generalized mechanics is established,the Euler-Lagrange equations are derived,the Hamiltonian is defined by using Legendre transformation,and the canonical equation are established.Secondly,the discriminant conditions of canonical transformation of second-order nonstand-ard generalized mechanics are established,and four basic forms of canonical transformation are given by different choices of generating functions.Finally,the Lie algebraic structure of second-order non-stand-ard generalized mechanics is verified,and Poisson theory of the first integral is established.Some exam-ples are given to demonstrate the application of the results.
关键词
广义力学/非标准Lagrange函数/正则变换/Poisson理论
Key words
generalized mechanics/non-standard Lagrangians/canonical transformation/Poisson theory
维普
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