Ebook: Analytical Mechanics: Translated from the Mécanique analytique, novelle édition of 1811

The Mécanique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.

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The M?canique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.

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The M?canique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.
Content:
Front Matter....Pages i-10
The Various Principles of Statics....Pages 11-26
A General Formula of Statics and its Application to the Equilibrium of an Arbitrary System of Forces....Pages 26-37
The General Properties of Equilibrium of a System of Bodies Deduced from the Preceding Formula....Pages 37-59
A More General and Simpler Way to Use the Formula of Equilibrium Presented in Section II....Pages 60-82
The Solution of Various Problems of Statics....Pages 82-136
The Principles of Hydrostatics....Pages 136-140
The Equilibrium of Incompressible Fluids....Pages 140-163
The Equilibrium of Compressible and Elastic Fluids....Pages 164-167
The Various Principles of Dynamics....Pages 169-184
A General Formula of Dynamics for the Motion of a System of Bodies Moved by Arbitrary Forces....Pages 184-190
General Properties of Motion Deduced from the Preceding Formula....Pages 190-223
Differential Equations for the Solution of All Problems of Dynamics....Pages 223-236
A General Method of Approximation for the Problems of Dynamics Based on the Variation of Arbitrary Constants....Pages 236-252
The Very Small Oscillations of an Arbitrary System of Bodies....Pages 253-305
The Motion of a System of Free Bodies Treated as Mass Points and Acted Upon by Forces of Attraction....Pages 311-442
The Motion of Constrained Bodies Which Interact in an Arbitrary Fashion....Pages 442-467
Rotational Motion....Pages 467-517
The Principles of Hydrodynamics....Pages 517-521
The Motion of Incompressible Fluids....Pages 521-560
The Motion of Compressible and Elastic Fluids....Pages 560-573
Back Matter....Pages 575-594

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The M?canique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.
Content:
Front Matter....Pages i-10
The Various Principles of Statics....Pages 11-26
A General Formula of Statics and its Application to the Equilibrium of an Arbitrary System of Forces....Pages 26-37
The General Properties of Equilibrium of a System of Bodies Deduced from the Preceding Formula....Pages 37-59
A More General and Simpler Way to Use the Formula of Equilibrium Presented in Section II....Pages 60-82
The Solution of Various Problems of Statics....Pages 82-136
The Principles of Hydrostatics....Pages 136-140
The Equilibrium of Incompressible Fluids....Pages 140-163
The Equilibrium of Compressible and Elastic Fluids....Pages 164-167
The Various Principles of Dynamics....Pages 169-184
A General Formula of Dynamics for the Motion of a System of Bodies Moved by Arbitrary Forces....Pages 184-190
General Properties of Motion Deduced from the Preceding Formula....Pages 190-223
Differential Equations for the Solution of All Problems of Dynamics....Pages 223-236
A General Method of Approximation for the Problems of Dynamics Based on the Variation of Arbitrary Constants....Pages 236-252
The Very Small Oscillations of an Arbitrary System of Bodies....Pages 253-305
The Motion of a System of Free Bodies Treated as Mass Points and Acted Upon by Forces of Attraction....Pages 311-442
The Motion of Constrained Bodies Which Interact in an Arbitrary Fashion....Pages 442-467
Rotational Motion....Pages 467-517
The Principles of Hydrodynamics....Pages 517-521
The Motion of Incompressible Fluids....Pages 521-560
The Motion of Compressible and Elastic Fluids....Pages 560-573
Back Matter....Pages 575-594
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