Methods of Analytical DynamicsA balanced presentation that encompasses both formalism and structure in analytical dynamics, this text also addresses solution methods. Its remarkably broad and comprehensive exploration of the subject employs an approach as natural as it is logical. In addition to material usually covered in graduate courses in dynamics and nonlinear mechanics, Methods of Analytical Dynamics presents selected modern applications. Contents include discussions of fundamentals of Newtonian and analytical mechanics, motion relative to rotating reference frames, rigid body dynamics, behavior of dynamical systems, geometric theory, stability of multi-degree-of-freedom autonomous and nonautonomous systems, and analytical solutions by perturbation techniques. Later chapters cover transformation theory, the Hamilton-Jacobi equation, theory and applications of the gyroscope, and problems in celestial mechanics and spacecraft dynamics. Two helpful appendixes offer additional information on dyadics and elements of topology and modern analysis. Book jacket. |
Contents
Preface | 1 |
Fundamentals of Analytical Mechanics | 45 |
Motion Relative to Rotating Reference Frames | 101 |
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a₁ angle angular momentum angular velocity angular velocity components assume body axes c₁ canonical center of mass coefficients const constant constraint contact transformation coordinates corresponding curve cyclic trajectory defined denoted derive differential equations dynamical earth eigenvalues equations of motion equilibrium point expression force frequency gimbal gravitational gyroscope Hamiltonian Hence inertia ellipsoid inertial space integral Introducing Eq Jacobi integral kinetic energy Lagrange Lagrange's equations Lagrangian Let us consider Liapunov function linear m₁ method moments of inertia neighborhood nonlinear obtain oscillator P₁ parameter particles periodic solution perturbation plane positive definite potential energy precession problem q₁ reduces referred relative represents respect rigid body rotation satellite second of Eqs second-order shown in Fig sin² singular point solution of Eq stability t₁ t₂ theorem torque unstable variables vector x₁ zero дак дяк