Canonical transformations and Poisson theory for second-order generalized mechanical systems with power-law Lagrangians

Abstract

The canonical transformation and Poisson theory for the second-order generalized mechanical systems based on non-standard power-law Lagrangians are studied. First, the Euler–Lagrange equations and the Hamilton canonical equations for the second-order generalized mechanics with the power-law Lagrangians are established. Second, the canonical transformation theory of the systems is studied by establishing the relationship between old and new variables. Four basic forms of canonical transformation are given, and the transformation formulas in each case are derived. Third, the algebraic structure of the dynamical equations of the systems is studied, and the corresponding Poisson theory is established. Finally, the corresponding examples are presented to illustrate the application of the results we obtained.