Lecture Notes on the Dynamics of Particles and
                        Rigid Bodies
                Class Notes for Engineering Mechanics III ME170
                    and Intermediate Dynamics ME175
                        Oliver M. O’Reilly
                                         To Anna
                                                      Contents
                         Preface                                                           page xi
                              Part I    Dynamics of a Single Particle                           1
                         1    Kinematics of a Single Particle                                   1
                              1.1   Introduction                                                1
                              1.2   Kinematics of a Particle                                    1
                              1.3   Frequently Used Coordinate Systems                          2
                                    1.3.1  Cartesian Coordinate System                          2
                                    1.3.2  Cylindrical Polar Coordinates                        3
                                    1.3.3  Spherical Polar Coordinates                          4
                              1.4   Curvilinear Coordinates                                     5
                                    1.4.1  Covariant Basis Vectors                              7
                                    1.4.2  Contravariant Basis Vectors                          7
                                    1.4.3  Covariant and Contravariant Components               8
                                    1.4.4  An Example                                           8
                                    1.4.5  Some Comments on Derivatives                         9
                              1.5   Representations of Particle Kinematics                     10
                              1.6   Integrable Constraints                                     12
                                    1.6.1  Some Examples                                       12
                                    1.6.2  The Canonical Case for an Integrable Constraint     13
                                    1.6.3  Curvilinear Coordinates and Integrable Constraints  16
                                    1.6.4  Further Examples of Integrable Constraints          17
                              1.7   Integrable Constraints and Non-Integrable Constraints      18
                                    1.7.1  Examples                                            19
                                    1.7.2  Integrability Criteria                              20
                              1.8   Exercises                                                  21
                         2    Kinetics of a Single Particle                                    26
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