Phase Volume and Canonicity Retention in Finite-Difference Gas Dynamic Schemes Constructed by the Sequential Variational Method

摘要

Phase volume and canonicity (hamiltonicity) are proved to be retained in finite-difference schemes of Lagrangian gas dynamics constructed by the sequential variational method using a formu- lation of the Hamilton–Ostrogradsky principle of the least action discrete in time and space. An example is given of finite-difference schemes which cannot be constructed by the sequential varia- tional method and in which for an arbitrary time-variable step and with any method for the selection of hidden generalized coordinates and hidden generalized momenta the phase volume is not retained and, therefore, canonicity is not preserved.