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- W145808467 abstract "Let M be a compact Lie group. The invariant scalar product (•, •) in the Lie algebra M = T Id M defines a left-invariant Riemannian structure on M: $${langle qu,qvrangle _q}_ = ^{def}langle u,urangle ,u,v in M,q in M,qu,qv in {T_q}M.$$So in every tangent space T q M there is a scalar product (•,•)q. For any Lipschitzian curve $$q:[0,1] to M$$its Riemannian length is defined as integral of velocity: $$iota = {text{ }}int_0^1 {left| {dot qleft( t right)} right|} dt,left| {dot q} right| = sqrt {langle dot q,dot qrangle } .$$" @default.
- W145808467 created "2016-06-24" @default.
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- W145808467 date "2004-01-01" @default.
- W145808467 modified "2023-10-05" @default.
- W145808467 title "Examples of Optimal Control Problems on Compact Lie Groups" @default.
- W145808467 doi "https://doi.org/10.1007/978-3-662-06404-7_19" @default.
- W145808467 hasPublicationYear "2004" @default.
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