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• W42648571 startingPage "129" @default.
• W42648571 abstract "The calculus of variations is concerned with finding extremal paths of functionals in analogy with the way that classical calculus seeks to find critical points of functions. Variational calculus plays a central role in classical mechanics, connecting the “Principle of Least Action” and Lagrange’s equations of motion (also called the Euler– Lagrange equations). In that setting, generalized coordinates are introduced to describe the geometric configuration of a mechanical system. In this chapter, classical variational calculus is reviewed and extended to describe systems on Lie groups. Of course, the introduction of coordinates such as Euler angles to describe the orientation of a rigid body can be used to formulate classical variational problems at the expense of introducing singularities. However, it is possible to formulate variational problems on Lie groups without coordinates. This results in the Euler’Poincaré equations." @default.
• W42648571 created "2016-06-24" @default.
• W42648571 creator A5012775344 @default.
• W42648571 date "2011-09-29" @default.
• W42648571 modified "2023-10-16" @default.
• W42648571 title "Variational Calculus on Lie Groups" @default.
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• W42648571 doi "https://doi.org/10.1007/978-0-8176-4944-9_4" @default.
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