Dynamics of the Rigid Solid with General Constraints by a Multibody Approach

1. Elements of Mathematical Calculation 1.1 Vectors; Vector Operations 1.2 Real Rectangular Matrix 1.3 Square Matrix 1.4 Skew Matrix of Third Order 2. Kinematics of the Rigid Solid 2.1 Finite Displacements of the Points of Rigid Solid 2.2 Matrix of Rotation; Properties 2.3 Minimum Displacements; The Chasles Theorem 2.4 Small Displacements 2.5 Velocities of the Points of Rigid Solid 2.6 The Angular Velocity Matrix; Properties 2.7 Composition of the Angular Velocities 2.8 Accelerations of the Points of Rigid Solid 3. General Theorems in the Dynamics of the Rigid Solid 3.1 Moments of Inertia 3.2 Momentum; The Theorem of Momentum 3.3 Moment of Momentum; The Theorem of Moment of Momentum 3.4 The Kinetic Energy of the Rigid Solid 4. Matrix Differential Equations of the Motion of Rigid Solid 4.1 The Differential Equations Obtained from the General Theorems 4.2 The Lagrange Equations in the Case of the Holonomic Constraints 4.3 The Equivalence between the Differential Equations Obtained from the General Theorems and the Lagrange Equations 4.4 The Matrix Differential Equations for the Motion of the Constrained Rigid Solid 5. Generalized Forces; The Equilibrium of the Rigid Solid 5.1 The Generalized Forces in the Case of a Mechanical System 5.2 The General Expressions of the Generalized Forces in the case of Rigid Solid 5.3 Conservative Forces 5.4 The Equilibrium of the Constrained Rigid Solid 5.5 The Equilibrium of the Heavy Rigid Solid Hanged by Springs 6. The Motion of the Rigid Solid with Constraints at Given Proper Points 6.1 General Aspects; Classification 6.2 Mathematical Aspects; Notations 6.3 The Study of the Rigid Solid with a Fixed Point 6.4 The Rigid Solid with Two Fixed Points (the Rotational Motion of the Rigid Solid) 6.5 The Rigid Solid with a Given Point Situated on a Fixed Surface 6.6 The Rigid Solid with Several Points Situated on Fixed Surfaces (Curves) 6.7 The Rigid Solid with a Fixed Point and with Another Point Situated on a Fixed Surface 6.8 The Rigid Solid with Two Given Points Situated on a Fixed Curve 7. The Motion of the Rigid Solid with Constraints on Given Proper Curves 7.1 General Aspects; Classification 7.2 The Rigid Solid Supported at Fixed Points on Given Proper Curves 7.3 The Rigid Solid at Which Given Proper Curves Support with Sliding on Fixed Curves 7.4 Rolling without Sliding of a Curve on a Fixed Curve 7.5 The Motion of the Rigid Solid at Which the Curves Jointed to It Support with Sliding on Fixed Surfaces 7.6 The Rolling without Sliding of a Disk Bounded by a Spatial Curve on a Fixed Surface 7.7 The Rolling without Sliding of a Planar Circle Disk on a Horizontal Plan 7.8 The Rolling without Sliding of a Planar Elliptic Disk on a Horizontal Plan 7.9 The Rolling without Sliding of a Hyperboidic Curve on a Horizontal Plan 7.10 The Rolling without Sliding of a Planar Circle Disk on a Cylindrical Surface with Horizontal Generatrices 7.11 The Rolling without Sliding of Two Curves of a Rigid Solid on a Fixed Surface 7.12 The Rolling without Sliding of an Axle with Wheels (Disks) with Angular Deviations on a Horizontal Plan 7.13 The Rolling without Sliding of an Axle with Disks on a Hyperbolic Paraboloid 8. The Motion of the Rigid Solid with Constraints on the Bounding Surface 8.1 General Aspects; Classification 8.2 The Rigid Solid Supported at Fixed Points 8.3 The Rigid Solid Supported with Sliding on Fixed Curves 8.4 The Rolling without Sliding of the Rigid Solid on Two Fixed Curves 8.5 The Rolling without Sliding of a Rigid Solid on a Fixed Surface 8.6 The Rolling without Sliding of a Toroidal Wheel on a Horizontal Plan 8.7 The Rolling without Sliding of a Rigid Solid Supported on Two Fixed Surfaces 8.8 The Rolling without Sliding of a Rigid Solid Supported at Two Points on a Fixed Surface Appendix Index