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https://hdl.handle.net/10316/11463
Título: | The Moser-Veselov equation | Autor: | Cardoso, J. R. Leite, F. Silva |
Palavras-chave: | Algebraic Riccati equation; Controllability; Stability; Primary matrix functions | Data: | 2001 | Editora: | Centro de Matemática da Universidade de Coimbra | Citação: | Pré-Publicações DMUC. 01-12 (2001) | Resumo: | We study the orthogonal solutions of the matrix equation XJ-JXT=M, where J is symmetric positive definite and M is skew-symmetric. This equation arises in the discrete version of the dynamics of a rigid body, investigated by Moser and Veselov [15]. We show connections between orthogonal solutions of this equation and solutions of a certain algebraic Riccati equation. This will bring out the symplectic geometry of the Moser-Veselov equation and also reduces most computational issues about solutions to finding invariant subspaces of a certain Hamiltonian matrix. Necessary and sufficient conditions for the existence of orthogonal solutions (and methods to compute them) are presented. Our method is contrasted with the Moser-Veselov approach presented in [15]. We also exhibit explicit solutions of a particular case of the Moser-Veselov equation, which appears associated with the continuous version of the dynamics of a rigid body. | URI: | https://hdl.handle.net/10316/11463 | Direitos: | openAccess |
Aparece nas coleções: | FCTUC Matemática - Artigos em Revistas Nacionais |
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Ficheiro | Descrição | Tamanho | Formato | |
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The Moser-Veselov equation.pdf | 217.83 kB | Adobe PDF | Ver/Abrir |
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