Variational Calculus on Lie Groups

摘要: The calculus of variations is concerned with finding extremal paths functionals in analogy the way that classical seeks to find critical points functions. Variational plays a central role mechanics, connecting “Principle Least Action” and Lagrange’s equations motion (also called Euler– Lagrange equations). In setting, generalized coordinates are introduced describe geometric configuration mechanical system. this chapter, variational reviewed extended systems on Lie groups. Of course, introduction such as Euler angles orientation rigid body can be used formulate problems at expense introducing singularities. However, it possible groups without coordinates. This results Euler’Poincare equations.