论文标题
时间依赖的能量摩托车法
A time-dependent energy-momentum method
论文作者
论文摘要
我们设计了能量动量方法的概括，用于研究具有哈密顿式对称性的谎言群体的非自治哈密顿系统的稳定性。提供并研究了对非自治领域的相对平衡点概念的概括。非自治哈密顿系统的相对平衡点是通过叶层谎言系统描述的，该系统打开了这种微分方程的新应用领域。我们通过Marsden-Weinstein定理降低了非自治的哈密顿系统，并提供条件，以确保相对平衡点的稳定性指向降低空间。作为一种应用，我们研究了一类机械系统的相对平衡点的稳定性，这涵盖了刚体作为特定实例。
We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a non-autonomous realm is provided and studied. Relative equilibrium points of non-autonomous Hamiltonian systems are described via foliated Lie systems, which opens a new field of application of such differential equations. We reduce non-autonomous Hamiltonian systems via the Marsden-Weinstein theorem and we provide conditions ensuring the stability of the projection of relative equilibrium points to the reduced space. As an application, we study the stability of relative equilibrium points for a class of mechanical systems, which covers rigid bodies as a particular instance.
