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 a class of non-autonomous Hamiltonian systems are described via foliated Lie systems, which opens a new field of application of such systems of 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 a byproduct, a geometrical extension of notions and results from Lyapunov stability theory on linear spaces to manifolds is provided. As an application, we study a class of mechanical systems, the hereafter called almost-rigid bodies, which covers rigid bodies as a particular instance.

我们设计了能量动量方法的推广，用于研究具有哈密顿对称李群的非自治哈密顿系统的稳定性。提供并研究了相对平衡点概念对非自治领域的推广。一类非自治哈密顿系统的相对平衡点是通过叶李系统来描述的，这开辟了此类微分方程系统的新应用领域。我们通过 Marsden-Weinstein 定理减少非自治哈密顿系统，我们提供了确保相对平衡点投影到减少空间的稳定性的条件。作为副产品，提供了从线性空间的李雅普诺夫稳定性理论到流形的概念和结果的几何扩展。作为应用程序，