Flexible multibody dynamics : efficient formulations and applications / Arun K. Banerjee.

6.4 Kinematical Recurrence Relations Pertaining to a Body and Its Inboard Body.

TitlePage; Copyright; Dedication; Preface; 1 Derivation of Equations of Motion; 1.1 Available Analytical Methods and the Reason for Choosing Kane's Method; 1.2 Kane's Method of Deriving Equations of Motion; 1.3 Comparison to Derivation of Equations of Motion by Lagrange's Method; 1.4 Kane's Method of Direct Derivation of Linearized Dynamical Equation; 1.5 Prematurely Linearized Equations and a Posteriori Correction by ad hoc Addition of Geometric Stiffness due to Inertia Loads; 1.6 Kane's Equations with Undetermined Multipliers for Constrained Motion.

1.7 Summary of the Equations of Motion with Undetermined Multipliers for Constraints1.8 A Simple Application; Appendix 1. A Guidelines for Choosing Efficient Motion Variables in Kane's Method; Problem Set 1; References; 2 Deployment, Station-Keeping, and Retrieval of a Flexible Tether Connecting a Satellite to the Shuttle; 2.1 Equations of Motion of a Tethered Satellite Deployment from the Space Shuttle; 2.2 Thruster-Augmented Retrieval of a Tethered Satellite to the Orbiting Shuttle; 2.3 Dynamics and Control of Station-Keeping of the Shuttle-Tethered Satellite.

Appendix 2.A Sliding Impact of a Nose Cap with a Package of Parachute Used for Recovery of a Booster Launching SatellitesAppendix 2.B Formation Flying with Multiple Tethered Satellites; Appendix 2.C Orbit Boosting of Tethered Satellite Systems by Electrodynamic Forces; Problem Set 2; References; 3 Kane's Method of Linearization Applied to the Dynamics of a Beam in Large Overall Motion; 3.1 Nonlinear Beam Kinematics with Neutral Axis Stretch, Shear, and Torsion; 3.2 Nonlinear Partial Velocities and Partial Angular Velocities for Correct Linearization.

3.3 Use of Kane's Method for Direct Derivation of Linearized Dynamical Equations3.4 Simulation Results for a Space-Based Robotic Manipulator; 3.5 Erroneous Results Obtained Using Vibration Modes in Conventional Analysis; Problem Set 3; References; 4 Dynamics of a Plate in Large Overall Motion; 4.1 Motivating Results of a Simulation; 4.2 Application of Kane's Methodology for Proper Linearization; 4.3 Simulation Algorithm; 4.4 Conclusion; Appendix 4.A Specialized Modal Integrals; Problem Set 4; References; 5 Dynamics of an Arbitrary Flexible Body in Large Overall Motion.

5.1 Dynamical Equations with the Use of Vibration Modes5.2 Compensating for Premature Linearization by Geometric Stiffness due to Inertia Loads; 5.3 Summary of the Algorithm; 5.4 Crucial Test and Validation of the Theory in Application; Appendix 5.A Modal Integrals for an Arbitrary Flexible Body [2]; Problem Set 5; References; 6 Flexible Multibody Dynamics: Dense Matrix Formulation; 6.1 Flexible Body System in a Tree Topology; 6.2 Kinematics of a Joint in a Flexible Multibody Body System; 6.3 Kinematics and Generalized Inertia Forces for a Flexible Multibody System.

Print version record.