蛤肉 发表于 2025-3-30 08:15:34
http://reply.papertrans.cn/23/2272/227162/227162_51.png放肆的你 发表于 2025-3-30 15:55:53
http://reply.papertrans.cn/23/2272/227162/227162_52.pngobstruct 发表于 2025-3-30 20:34:56
Action-Angle Variables,necessarily . = α.. But the . are, like the α., constants. On the other hand, . develops linear with time: . with constants . = .(.) and β.. The transformation equations which are associated with the above canonical transformation generated by .(., .) are given byIsthmus 发表于 2025-3-30 20:58:19
http://reply.papertrans.cn/23/2272/227162/227162_54.png其他 发表于 2025-3-31 02:50:45
The Action Principles in Mechanics,.. , ., are points in .-dimensional configuration space. Thus .(.) describes the motion of the system, and . determines its velocity along the path in configuration space. The endpoints of the trajectory are given by .(.) = ., and .(.) = ..Excitotoxin 发表于 2025-3-31 08:20:03
Jacobi Fields, Conjugate Points,particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space. If we parametrize the path between points . and . by ϑ, then Jacobi’s princidelegate 发表于 2025-3-31 09:57:05
http://reply.papertrans.cn/23/2272/227162/227162_57.png关节炎 发表于 2025-3-31 14:56:50
Action-Angle Variables, .) is the generator of a canonical transformation to new constant momenta . (all . are ignorable), and the new Hamiltonian depends only on the .: . = . = .(.). Besides, the following canonical equations are valid: . The . are . independent functions of the . integration constants α., i.e., are not走路左晃右晃 发表于 2025-3-31 20:30:20
http://reply.papertrans.cn/23/2272/227162/227162_59.png纬线 发表于 2025-4-1 01:36:37
http://reply.papertrans.cn/23/2272/227162/227162_60.png