Topics in the Geometric Theory of Integrable Mechanical Systems (Hermann, Robert//Interdisciplinary Mathematics vol.23)
By Robert Hermann
* Publisher: Math Science Pr
* Number Of Pages: 347
* Publication Date: 1985-01
* ISBN-10 / ASIN: 0915692368
* ISBN-13 / EAN: 9780915692361
* Binding: Hardcover
Approximate Contents :
(CHAPTER TITLE / page number / keyword, keyword, keyword )
INTEGRABILITY IN TERMS OF THE HAMILTONJACOBI EQUATIONS
1
ordinary differential equation, action-angle variables, Hamilton-Jacobi equation
in Terms of Symplectic Manifold Theory and Cartans Theory
9
Hamilton equations, symplectic manifold, Abelian integrals
INTEGRABLE HAMILTONIAN SYSTEMS OF THE STACHEL TYPE
33
symplectic manifold, Poisson bracket, Hamiltonian
GEOMETRIC STRUCTURES IN INTEGRABILITY THEORY
47
vector bundle, cotangent bundle, differential equations
EHRESMANN PSEUDOGROUPS AND FOLIATIONS
59
pseudogroup, tensor field, local diffeomorphism
LINEAR DIFFERENTIAL OPERATORS AND PARTIAL WAVE ANALYSIS
75
Lie group, group action, linear differential operators
LIES FUNCTION GROUPS AND POISSON STRUCTURES ON MANIFOLDS
83
bivector, Function Groups, Schouten tensor
PICARDVESSIOT THEORY
97
Picard-Vessiot Theory, differential equation, equivalence relation
The Classical PicardVessiot Theory
107
rational maps, Differential Algebra, monodromy group
RELATIONS BETWEEN KORTEWEGDE VRIES AND PICARDVESSIOT
111
Picard-Vessiot theory, linear subspace, associative algebra
The Muira Transform
117
Moyal product, invariant theory, linear map
THE GENERALIZED TODA LATTICES AS CAUCHY CHARACTERISTIC
125
Toda lattice, absolute parallelism, REDUCTIVE LIE ALGEBRAS
Jacobi Triples of Lie Algebras
131
Toda lattice, semisimple Lie algebra, simple root
TOWARD THE GEOMETRIC UNIFICATION OF OPTIMAL CONTROL
143
Grassmann algebra, calculus of variations, differential forms
The First and Second Variation for Canonical Variational
150
calculus of variations, differential forms, VARIATIONAL PROBLEMS
Newtons Laws and Characteristics of TwoDifferential Forms
156
Grassmann algebra, two-differential form, equivalence relation
When is the TwoDifferential Form Defined by the Newton
162
closed differential form, optimal control, symplectic structure
Maxwells Equations
170
Lorentz metric, Maxwell's equations, inner product
MAXWELLS ELECTROMAGNETIC EQUATIONS AND ANALYTICAL MECHANICS Introduction
177
First Variation of the Lagrangian and Maxwells Equations
178
Kinetic and Potential Energy in Newtonian Mechanics
181
Kinetic and Potential Energy for Maxwell Fields
182
Lorentz metric, Maxwell's Equations, potential energy
Force in Newtonian Particle Mechanics in Terms of the Calculus of Variations
184
Riccati equation, stochastic differential equation, optimal control
PERIODIC SOLUTIONS FOR THE MATRIX RICCATI EQUATION VIA LIE THEORY 1 Introduction
189
Lie theory, control theory, symmetric matrices
Certain Types of Periodic Orbits as Fixed Points
190
Riccati equations, diffeomorphism, eigenvalues
A LieTheoretic Situation
192
nontrivial periodic orbits, transformation group action, LIE-THEORETIC
The Case where GH is a Coset Space such that GH is a Grassmann Pair
193
Grassmann manifold, Killing form, Lie subgroup
Periodic Orbits of Certain Vector Fields on Compact 1 Homogeneous Spaces
195
periodic orbits, grad(f, fixed point
Classes of Vector Fields on the LagrangeGrassmann Manifold that have Periodic Orbits
196
eigenvalues, Riccati equat, coset
STOCHASTIC SYSTEMS 189 18 190 192 193 195 196 Chapter
201
Kalman-Bucy filter, STOCHASTIC SYSTEMS, theory
DIFFERENTIAL GEOMETRY AND LIE THEORY OF CLASSICAL AND QUANTUM STOCHASTIC SYSTEMS 1 Introduction
203
quantum mechanical, physicists, manifold
Diffusion Equations on Manifolds
205
DIFFUSION EQUATIONS, deterministic, suppose that d6
Quantum Diffusion Operators
207
Hermitian, QUANTUM DIFFUSION OPERATORS, linear
The Algebra of the Quantum Mechanical FP Operators
208
tensor product, QUANTUM MECHANICAL, associative algebra structure
Some Classical and Quantum Operators of FPType 6 InfeldHull Factorization and Solution of Linear Evolution Equations
210
quantum mechanical, integral operator, degree of freedom
Factoring Second Order Differential Operators in Commutative Differential Algebras
215
differential algebra, DIFFERENTIAL OPERATORS, scalars
Differential Equations whose Lie Algebras are Finite Dimensional
217
Lie subalgebra, subalgebra of 2I, FINITE DIMENSIONAL
Generalization of the FockBargmannSegal Construction
218
polynomial, constant coefficients, another Lie algebra
An Abstract Form of PicardVessiot Theory
221
PICARD-VESSIOT THEORY, differential structure, scalar field
Factoring Second Order Differential Operators with Rational Coefficients
223
rational functions, Galois group, analytic functions
The InfeldHull Factorization of the Bessel Equation
226
BESSEL EQUATION, INFELD-HULL, d/dz
The InfeldHull Factorization of the Bessel Equation in Terms of Deformation Theory
228
subspace spanned, one-parameter family, FACTORIZATION
The InfeldHull Factorization for the Whittaker Equation
229
INFELD-HULL, WHITTAKER, functions
The Lie Algebra and InfeldHull Structure for the Legendre Function
230
Whittaker functions, algebraic curve, Riemann surface
The Lie Algebra of the InfeldHull Relations in Terms of the Rational Enveloping Algebras of Finite Dimensional Lie Algebras
231
Riemann surface, Lie algebra SP, Infeld-Hull factorization
Quantum Stochastic Systems whose Deterministic Part is
233
HARMONIC OSCILLATOR, Hermitian, adjoint
Harmonic Oscillator in the FockSegal Representation References
237
probability measure, Stochastic Differential Equations, Differential Algebra
KRONKONDO THEORY
255
Gabriel Kron, covariant derivative, differential manifold
Generalized Linear InputOutput Systems and Covariant
261
Pfaffian system, LAGRANGIAN MECHANICAL, moving frame
CYCLIC COORDINATES AND LINEAR SYSTEMS _
269
Cyclic Coordinates, Lagrange's equations, degrees of freedom
DIFFERENTIAL GEOMETRY OF ENGINEERINGMECHANICS SYSTEMS
291
Lagrangian mechanics, Lagrange equations, Pfaffian
NEWTONLAGRANGE LINEAR SYSTEMS
309
circuit theory, electrical circuit, LINEAR SYSTEMS
THE GEOMETRIC NATURE OF POWER IN LAGRANGIAN MECHANICS
315
coordinate system, cotangent, bundle to Q
THE RLC EQUATION IN GEOMETRIC FORM
323
RATIONAL MAP, non-singular, RLC Equations
GEOMETRIC STRUCTURE IN FIELD THEORY
331
function groups, dual bundle, quotient space
The Volterra Formalism in Local Coordinates
337
Volterra, local coordinates
Volterra Tensors
343
tensor, linear functions, Cojet Bundles
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