We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to generator matrices and their usefulness in many manipulations. The example of rigid body rotation, i.e. motion on the Lie group SO(3), is used as an example, and it is shown how to derive Euler's equations directly from the principle of least action. The techniques covered in this paper generalize to other Lie groups in a straightforward manner, which is discussed. We briefly discuss the Hamiltonian formulation of the problem as well.
Nonconservative Lagrangian mechanics II: purely causal equations of motion
这项工作建立在[D. W. Dreisigmeyer和P.M. Young，J. Phys. A \textbf{36}，8297，（2003）]来模拟非保守系统。在这里，我们把拉格朗日和行动作为“时间依赖”Volterra系列。我们提出了一个新的用于这些Volterra级数的核族，使我们能够使用变分原理推导出单个延迟运动方程。
Objectivity in continuum mechanics, an introduction. Motions, Eulerian and Lagrangian variables and functions, deformation gradient, Lie derivatives, velocity-addition formula, Coriolis
