论文标题
联系几何力学：Tulczyjew Triples
Contact geometric mechanics: the Tulczyjew triples
论文作者
论文摘要
我们提出将经典Tulczyjew Triple作为哈密顿和拉格朗日形式主义的几何工具的概括，这些工具用于接触歧管。 Tulczyjew案中Cotangent Bundles上的规范符号结构的rol是由捆绑包的$ j^1l $ j^1l $ j^1 l LINE BUNDLES $ l \ l \ to M $的第一个部分的$ J^1 l $播放的。联系哈密顿量和联系人拉格朗日人被认为是某些线束的部分，他们确定接触阶段空间$ j^1l $的（通常是隐式的）动态。我们还研究了Legendre地图的触点类似物以及在两个接触形式主义中生成对象的Legendre转换。提供了几个明确的例子。
We propose a generalization of the classical Tulczyjew triple as a geometric tool in Hamiltonian and Lagrangian formalisms which serves for contact manifolds. The rôle of the canonical symplectic structures on cotangent bundles in Tulczyjew's case is played by the canonical contact structures on the bundles $J^1L$ of first jets of sections of line bundles $L\to M$. Contact Hamiltonians and contact Lagrangians are understood as sections of certain line bundles, and they determine (generally implicit) dynamics on the contact phase space $J^1L$. We also study a contact analog of the Legendre map and the Legendre transformation of generating objects in both contact formalisms. Several explicit examples are offered.
