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    93B10 - Canonical structure
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Libro

Geometric structure theory of systems--control theory and physics

Robert Hermann.

Brookline, Mass. : Math Sci Press, ©1974-<©1976 >.

    v. ; 21 cm.

Serie: Interdisciplinary mathematics ; v. 9, 11

ISBN: 0915692147 (pt. B)

Título en cubiertas y en portada de pt. B: Geometric structure of systems--control theory and physics

Bibliografía: v. 1, p. 439-442.

Reseña: MathSciNet, 58 #33186 (pt. A)
MathSciNet, 58 #33269 (pt. B)

Contenido

  • Chapter I, Lie's theory of groups and differential equations; Chapter II, Dissipative mechanical systems and electrical networks; Chapter III, Pfaffian, vector field and Monge systems; Chapter IV, The Carathéodory approach to the calculus of variations; Chapter V, Optimal control variational problems; Chapter VI, Singular characteristics curves of closed 2-forms and optimal control variational problems; Chapter VII, The algebra of boundary conditions for linear ordinary differential equations; Chapter VIII, The Kronecker theory of systems of linear, time-invariant ordinary differential equations; Chapter IX, The geometry of interactions in thermodynamics; Chapter X, The geometry of interaction in classical mechanics; Chapter XI, Differential-geometric interconnection of systems and electrical circuits; Chapter XII, The theory of network parts; Chapter XIII, Controllability and observability of input-output systems.
  • Chapter 1. The Carathéodory approach to optimal control variational problems, and the Pontrjagin minimal principle; Chapter 2. Hamilton-Jacobi theory and the optimal control problem; Chapter 3. Characteristic curves and the first and second variation formulas for optimal control problems; Chapter 4. The Weierstrass condition and the Pontrjagin principle; Chapter 5. An optimal-control distributed-parameter and field-theoretic variational problem; Chapter 6. A general form of circuit theory; Chapter 7. The equations of motion of mechanical systems; Chapter 8. Abelian groups of Lagrangian symmetries and cyclic coordinates; Chapter 9. Some relations between analytical and quantum mechanics; Chapter 10. The quantization conditions of Bohr, Sommerfeld and Einstein; Chapter 11. Canonical transformations generated by complete solutions of the Hamilton-Jacobi equation; Chapter 12. Invariant integrals and continuum mechanics; Chapter 13. Optimization and programming of functions on manifolds; Chapter 14. Optimization of functions under constraints; Chapter 15. Pareto optimals and extremals.
 
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