1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo of distributions Cartan's approach The tangent cone and Carnot groups Discrete groups tending to Carnot geometries Open problems Mechanics and geometry of bundles: Metrics on bundles Classical particles in Yang-Mills fields Quantum phases Falling, swimming, and orbiting Appendices: Geometric mechanics Bundles and the Hopf fibration The Sussmann and Ambrose-Singer theorems Calculus of the endpoint map and existence of geodesics Bibliography Index.

A Tour of Subriemannian Geometries, Their Geodesics and Applications

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a description of its features, and a discussion of select submodules. The supplementary material provide additional examples and further outline details of the architecture and features of SymPy.

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SymPy: Symbolic Computing in Python

In this paper, we propose a new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD/sup 2/ feedback structure, where the proportional action is in terms of the vector quaternion and the two derivative actions are in terms of the airframe angular velocity and the vector quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the vector-quaternion and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. The proposed controller as well as some other controllers have been tested experimentally on a small-scale quadrotor aircraft.

Attitude stabilization of a VTOL quadrotor aircraft

Dynamics : theory and applications

The behavior of a cantilever beam built into a rigid body that is performing a specified motion of rotation and translation is studied with two objectives in mind. First, because the subject is of interest in connection with spacecraft antennae, helicopter rotor blades, robot arms, and other systems that perform complex motions, we create an algorithm that can be used to predict the behavior of the beam when the base undergoes general three-dimensional motions. Effects such as centrifugal stiffening and vibrations induced by Coriolis forces are accommodated automatically, rather than with the aid of ad hoc provisions. The second objective is to draw attention to fundamental flaws in certain multibody computer programs currently under development or already in use. To this end, we construct a second simulation algorithm, one that embodies the procedure apparently employed in the programs in question, and then compare simulation results produced by computer programs based on the two algorithms. Conflicts between the two approaches that thus come to light are discussed in detail.

Dynamics of a cantilever beam attached to a moving base

Extensive experience has shown that the use of general- purpose, multibody-dynamics computer programs for the numerical formulation and solution of equations of motion of robotic devices leads to s...

The Use of Kane's Dynamical Equations in Robotics:

HE formulation of equations of motion, always an important facet of spacecraft design and performance analysis, is receiving ever greater attention as vehicles become larger and more complex and as the need grows more and more acute to predict spacecraft motions accurately. This article is intended to answer the following question that is clearly central in this context: "What are the relative advantages of various methods available for the formulation of equations of motion of complex spacecraft?" The question just stated can be answered incisively only if the criteria by which a given method is judged are sufficiently well defined, and meaningful criteria can be established only after a clear-cut purpose for the formulation of equations of motion has been identified. We take this purpose to be the production of algorithms to be employed for the simulation of spacecraft motions by means of numerical solutions of initial value problems. The principal criteria by which we judge a method are the simplicity of the equations to which it leads and the amount of labor required for the formulation of the equations. Of course, neither criterion is important when one is dealing with a relatively uncomplicated system. Conversely, these matters can become crucial in connection with truly complex spacecraft, for both computer storage limitations and excessive execution times can then plague one needlessly if equations have not been brought into the simplest possible form, and the labor expended to generate equations which have such a form can easily become prohibitive unless a highly efficient scheme for formulating equations of motion has been employed from the outset. It should be understood, therefore, that we are not concerned with systems so simple that their equations of motion can be produced with essentially equal ease by using almost any method. Since there exist numerous so-called multibpdy programs, as well as analyses intended to be the bases for such programs, and it is quite clear that these are of great value in solving problems of spacecraft dynamics, one may well ask whether or not it is ever really necessary to construct literal equations of motion for complex vehicles. The answer is that the need to do this arises frequently because multibody programs can fail a user in a number of ways. Every such program represents a compromise between two mutually exclusive goals, that of providing a computer code applicable to the solution of the widest possible class of problems, and that of minimizing the effort required by a user to bring his problem into a form compatible with program input requirements. Consequently, a given multibody program can be totally inapplicable to a particular problem, can force a user to make major program additions or other modifications, or can lead to inefficient or inaccurate simulations. Clearly, therefore, algorithms created to meet specific needs are indispensable. Not surprisingly, it is precisely the authors of some of the best multibody programs who, realizing all of this, welcome algorithms developed independently, particularly since these can be used to test the validity of multibody computer codes. Moreover, although it is probably true that the greatest obstacle to be surmounted in producing a multibody program is that of devising a procedure for assembling the equations of motion associated with the various bodies comprising a spacecraft, rather than that of writing equations governing the behavior of a generic body, there can be little doubt that the way in which the latter

Formulation of Equations of Motion for Complex Spacecraft

http://pentagono.uniandes.edu.co/~jarteaga/geosem/taller7/minicursoJK-Uniandes/robotic%20examples/kane.pdf

Thomas R. Kane

Papers

Dynamics : theory and applications

Dynamics of a cantilever beam attached to a moving base

The Use of Kane's Dynamical Equations in Robotics:

Formulation of Equations of Motion for Complex Spacecraft

A dynamical explanation of the falling cat phenomenon