Mathematical Methods for Mechanics

Cover -- Contents -- Chapter 1. Mathematical Auxiliaries -- 1.1. Matrix Computations -- 1.2. Brief on Vector Analysis -- 1.3. Curves in R3 -- 1.4. Linear Differential Equations -- 1.5. Linear Differential Systems of First Order -- 1.6. The Flux Integral and its Vector Field -- 1.7. Vector Spaces -- 1.8. Derivatives -- 1.9. Mappings in Banach Spaces -- 1.10. Convex Sets and Functions -- 1.11. Quadratic Functionals -- Chapter 2. Numerical Methods -- 2.1. Interpolation and Approximation -- 2.2. Orthogonal Polynomials -- 2.3. Numerical Integration -- 2.4. Initial Value Problems -- 2.5. Boundary Value Problems -- 2.6. Periodic Problems -- 2.7. Differential Algebraic Problems -- 2.8. Hints to the MATLAB Programs -- Chapter 3. Optimization -- 3.1. Minimization of a Function -- 3.2. Extrema with Constraints -- 3.3. Linear Programming -- 3.4. Linear-Quadratic Problems -- 3.5. Nonlinear Optimization -- 3.6. A Brief on Lagrange Theory -- 3.7. Hints to the MATLAB Programs -- Chapter 4. Variation and Control -- 4.1. Variation -- 4.2. Control Problems without Constraints -- 4.3. Control Problems with Constraints -- 4.4. Examples -- 4.5. On the Re-Entry Problem -- 4.6. Hints to the MATLAB Programs -- Chapter 5. The Road as Goal -- 5.1. Bifurcation Problems -- 5.2. Scaling -- 5.3. Calculation of Singular Points -- 5.4. Ordinary Differential Systems -- 5.5. Hopf Bifurcation -- 5.6. Numerical Bifurcation -- 5.7. Continuation -- 5.8. Hints to the MATLAB Programs -- Chapter 6. Mass Points and Rigid Bodies -- 6.1. The Force and its Moment -- 6.2. Dynamics of a Mass Point -- 6.3. Mass Point in Central Field -- 6.4. Systems of Mass Points -- 6.5. The Three-Body Problem -- 6.6. Rotating Frames -- 6.7. Inertia Tensor and Top -- 6.8. On Multibody Problems -- 6.9. On Some Principles of Mechanics -- 6.10. Hints to the MATLAB Programs -- Chapter 7. Rods and Beams -- 7.1. Bending Beam -- 7.2. Eigenvalue Problems -- 7.3. Numerical Approximation -- 7.4. Frameworks of Rods -- 7.5. Frameworks of Beams -- 7.6. Hints to the MATLAB Programs -- Chapter 8. Continuum Theory -- 8.1. Deformations -- 8.2. The Three Transport Theorems -- 8.3. Conservation Laws -- 8.4. Material Forms -- 8.5. Linear Elasticity Theory -- 8.6. Discs -- 8.7. Kirchhoffs Plate -- 8.8. Von Karmans Plate and the Membrane -- 8.9. On Fluids and Gases -- 8.10. Navier-Stokes Equations -- Chapter 9. Finite Elements -- 9.1. Elliptic Boundary Value Problems -- 9.2. From Formula to Figure, Example -- 9.3. Constructing Finite Elements -- 9.4. Further Topics -- 9.5. On Singular Elements -- 9.6. Navier-Stokes Equations -- 9.7. Mixed Applications -- 9.8. Examples -- 9.9. Hints to the MATLAB Programs -- Chapter 10. A Survey on Tensor Calculus -- 10.1. Tensor Algebra -- 10.2. Algebra of Alternating Tensors -- 10.3. Differential Forms in Rn -- 10.4. Tensor Analysis -- 10.5. Examples -- 10.6. Transformation Groups -- Chapter 11. Case Studies -- 11.1. An Example of Gas Dynamics -- 11.2. The Reissner-Mindlin Plate -- 11.3. Examples of Multibody Problems -- 11.4. Dancing Discs -- 11.5. Buckling of a Circular Plate -- Chapter 12. Appendix -- 12.1. Notations and Tabl.