Rigid Body Dynamics

  1. Three-Dimensional Kinetics of a Rigid Body
    1. Mass Moments and Products of Inertia
      1. Moments of Inertia
        1. Products of Inertia
          1. Inertia Tensor
            1. Definition and Properties
              1. Calculation for Simple Bodies
              2. Principal Axes
                1. Principal Moments of Inertia
                  1. Parallel-Axis Theorem in 3D
                    1. Parallel-Plane Theorem
                    2. Angular Momentum in 3D
                      1. General Expression
                        1. Relationship between Angular Momentum and Angular Velocity
                          1. Angular Momentum about Different Points
                          2. Equations of Motion in 3D
                            1. Force Equation
                              1. Moment Equation
                                1. Application to Rigid Bodies
                                2. Euler's Equations of Motion
                                  1. Derivation for a Body-Fixed Frame
                                    1. Application to Principal Axes
                                      1. Physical Interpretation
                                      2. Motion about a Fixed Point
                                        1. Gyroscopic Motion
                                          1. Precession
                                            1. Nutation
                                              1. The Gyroscope
                                                1. Gyroscopic Couple
                                                  1. Applications in Engineering
                                              2. General 3D Motion Analysis
                                                1. Combined Translation and Rotation
                                                  1. Problem Solving Techniques

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                                                6. Three-Dimensional Kinematics of a Rigid Body

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                                                8. Advanced Topics and Applications