科研之友
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摘要
Riemannian cubics are curves in Riemannian manifolds M that are critical points for the L (2) norm of covariant acceleration, and are already rather well studied as elementary curves for interpolation problems in engineering. In the present paper the L (2) norm is replaced by the L (a) norm, which may be more appropriate for some applications. However it is more difficult to derive the analogue of the Euler-Lagrange equation for the L (a) norm, requiring techniques from optimal control, and the resulting necessary conditions take a different form. These necessary conditions are examined when M is a sphere or a bi-invariant Lie group, and some examples are given.
- 出版日期2014-8
