Abstract:In this paper, we studied the canonical transformations of secondorder nonstandard generalized mechanics with exponential Lagrangians and Poisson theory on the first integrals. First, Hamilton principle of secondorder nonstandard generalized mechanics is established, the EulerLagrange 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 secondorder nonstandard 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 secondorder nonstandard generalized mechanics is verified, and Poisson theory of the first integral is established. Some examples are given to demonstrate the application of the results.