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High-order integrators for Lagrangian systems on homogeneous spaces via nonholonomic mechanics by Rodrigo T. Sato Martín de Almagro is a Mathematics article available to read on EtoBox.
What is High-order integrators for Lagrangian systems on homogeneous spaces via nonholonomic mechanics about?
In this paper, high-order numerical integrators on homogeneous spaces will be presented as an application of nonholonomic partitioned Runge–Kutta Munthe-Kaas (RKMK) methods on Lie groups. A homogeneous space M is a manifold where a group G acts transitively. Such a space can be understood as a quotient M ≅ G / H , where a closed Lie subgroup H , is the isotropy group of each point of M . The Lie algebra of G may be decomposed into g = m ⊕ h , where h is the subalgebra that generates H and m is a subspace spanning the tangent spaces of M . Thus, variational problems on M can be treated as nonholonomically constrained problems on G , by requiring variations to remain on m . Nonholonomic partitioned RKMK integrators are derived as a modification of those obtained by a discrete variational principle on Lie groups, and can be interpreted as obeying a discrete Chetaev principle. These integrators tend to preserve several properties of their purely variational counterparts.
Who reads High-order integrators for Lagrangian systems on homogeneous spaces via nonholonomic mechanics?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Rodrigo T. Sato Martín de Almagro
- Publisher
- Elsevier BV
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)