The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are...The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.展开更多
1 Introduction The transformation theory is an important method to study the problem of analytical mechanics as well as a theory of dynamics. For the Hamiltonian systems, we always hope that one can use the transforma...1 Introduction The transformation theory is an important method to study the problem of analytical mechanics as well as a theory of dynamics. For the Hamiltonian systems, we always hope that one can use the transformation to make the equations simplified, integrable or to turn them into the form convenient for study without changing the structure of canonical equa-展开更多
This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,...This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.展开更多
基金Supported by the National Natural Science Foundation of China(12272248,11972241)。
文摘The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.
基金Project supported by the National Natural Science Foundation of China.
文摘1 Introduction The transformation theory is an important method to study the problem of analytical mechanics as well as a theory of dynamics. For the Hamiltonian systems, we always hope that one can use the transformation to make the equations simplified, integrable or to turn them into the form convenient for study without changing the structure of canonical equa-
文摘This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.
