Variational Principles of Mechanics

ISBN-10: 0486650677

ISBN-13: 9780486650678

Edition: Reprint 

Authors: Cornelius Lanczos

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Book details

List price: $22.95
Publisher: Dover Publications, Incorporated
Publication date: 3/1/1986
Binding: Paperback
Pages: 464
Size: 5.50" wide x 8.50" long x 1.00" tall
Weight: 1.034
Language: English

&nbsp Introduction
The variational approach to mechanics
The procedure of Euler and Lagrange
Hamilton's procedure
The calculus of variations
Comparison between the vectorial and the variational treatments of mechanics
Mathematical evaluation of the variational principles
Philosophical evaluation of the variational approach to mechanics
The Basic Concepts of Analytical Mechanics
The Principal viewpoints of analytical mechanics
Generalized coordinates
The configuration space
Mapping of the space on itself
Kinetic energy and Riemannian geometry
Holonomic and non-holonomic mechanical systems
Work function and generalized force
Scleronomic and rheonomic systems
The law of the conservation of energy
The Calculus of Variations
The general nature of extremum problems
The stationary value of a function
The second variation
Stationary value versus extremum value
Auxiliary conditions
The Lagrangian lambda-method
Non-holonomic auxiliary conditions
The stationary value of a definite integral
The fundamental processes of the calculus of variations
The commutative properties of the delta-process
The stationary value of a definite integral treated by the calculus of variations
The Euler-Lagrange differential equations for n degrees of freedom
Variation with auxiliary conditions
Non-holonomic conditions
Isoperimetric conditions
The calculus of variations and boundary conditions
The problem of the elastic bar
The principle of virtual work
The principle of virtual work for reversible displacements
The equilibrium of a rigid body
Equivalence of two systems of forces
Equilibrium problems with auxiliary conditions
Physical interpretation of the Lagrangian multiplier method
Fourier's inequality
D'Alembert's principle
The force of inertia
The place of d'Alembert's principle in mechanics
The conservation of energy as a consequence of d'Alembert's principle
Apparent forces in an accelerated reference system
Einstein's equivalence hypothesis
Apparent forces in a rotating reference system
Dynamics of a rigid body
The motion of the centre of mass
Dynamics of a rigid body
Euler's equations
Gauss' principle of least restraint
The Lagrangian equations of motion
Hamilton's principle
The Lagrangian equations of motion and their invariance relative to point transformations
The energy theorem as a consequence of Hamilton's principle
Kinosthenic or ignorable variables and their elimination
The forceless mechanics of Hertz
The time as kinosthenic variable; Jacobi's principle; the principle of least action
Jacobi's principle and Riemannian geometry
Auxiliary conditions; the physical significance of the Lagrangian lambda-factor
Non-holonomic auxiliary conditions and polygenic forces
Small vibrations about a state of equilibrium
The Canonical Equations of motion
Legendre's dual transformation
Legendre's transformation applied to the Lagrangian function
Transformation of the Lagrangian equations of motion
The canonical integral
The phase space and the space fluid
The energy theorem as a consequence of the canonical equations
Liouville's theorem
Integral invariants, Helmholtz' circulation theorem
The elimination of ignorable variables
The parametric form of the
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