Tangent bundle geometry Lagrangian dynamics
Tangent bundle geometry Lagrangian dynamics
复制标题
切丛几何拉格朗日动力学
DOI：
--
复制
发表时间：
1983
期刊：
影响因子：
--
通讯作者：
M. Crampin
中科院分区：
文献类型：
--
作者：
M. Crampin
检查可微流形的切丛的微分几何的各个方面，并将结果应用于与时间无关的拉格朗日动力学。结果表明，某种类型的 (1, 1) 张量场是切丛本征几何的一部分，是切向量投影图的张量等价物，在拉格朗日理论中的作用几乎不亚于哈密顿理论中余切丛上的正则一式。拉格朗日理论的最新结果是从这个新观点来解释的。
Various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined, and the results applied to time-independent Lagrangian dynamics. It is shown that a certain type (1, 1) tensor field which is part of the intrinsic geometry of a tangent bundle, being a tensorial equivalent of the projection map of tangent vectors, plays a role in Lagrangian theory scarcely less important than that of the canonical one-form on a cotangent bundle in Hamiltonian theory. Recent results in Lagrangian theory are interpreted from this new viewpoint.