Riemannian cubics close to geodesics at the boundaries
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Publication:2086015
DOI10.3934/jgm.2022003OpenAlexW4213071197MaRDI QIDQ2086015
Margarida Camarinha, Leite Fátima Silva, Peter E. Crouch
Publication date: 20 October 2022
Published in: Journal of Geometric Mechanics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/jgm.2022003
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Geodesics in global differential geometry (53C22) Approximation by polynomials (41A10) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Lagrange's equations (70H03) Methods of local Riemannian geometry (53B21)
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Cites Work
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- Geometric mean and geodesic regression on Grassmannians
- Approximating near-geodesic natural cubic splines
- Geometric integrators for higher-order variational systems and their application to optimal control
- Higher-order smoothing splines versus least squares problems on Riemannian manifolds
- Optimal control on Riemannian manifolds by interpolation
- Invariant higher-order variational problems. II
- The Euler-Lagrange method for biharmonic curves
- Dynamic coverage optimal control for multiple spacecraft interferometric imaging
- Bi-Jacobi fields and Riemannian cubics for left-invariant \(\mathrm{SO}(3)\)
- Higher order geodesics in Lie groups
- On the geometry of Riemannian cubic polynomials.
- Elastic curves as solutions of Riemannian and sub-Riemannian control problems.
- The variational discretization of the constrained higher-order Lagrange-Poincaré equations
- The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces
- Existence of variationally defined curves with higher order elliptic Lagrangians
- Neighboring extremal optimal control for mechanical systems on Riemannian manifolds
- About simple variational splines from the Hamiltonian viewpoint
- Variational point-obstacle avoidance on Riemannian manifolds
- Shape splines and stochastic shape evolutions: A second order point of view
- Cubic polynomials on Lie groups: reduction of the Hamiltonian system
- Quadratures and cubics in SO(3) and SO(1,2)
- A Geometric Approach to the Optimal Control of Nonholonomic Mechanical Systems
- Cubic Splines on Curved Spaces
- Unit speed stationary points of the acceleration
- A Numerical Algorithm for $C^2$-Splines on Symmetric Spaces
- Null cubics and Lie quadratics
- Dynamic interpolation for obstacle avoidance on Riemannian manifolds
- Variational time discretization of Riemannian splines
- Combined homotopy and neighboring extremal optimal control
