Variational Methods and Complementary Formulations in Dynamics

C. Tabarrok, F.P. Rimrott (Autoren)

Buch | Softcover

368 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1994
Springer (Verlag)
978-90-481-4422-8 (ISBN)

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Not many disciplines can c1aim the richness of creative ideas that make up the subject of analytical mechanics. This is not surprising since the beginnings of analyti cal mechanics mark also the beginnings of the theoretical treatment of other physical sciences, and contributors to analytical mechanics have been many, inc1uding the most brilliant mathematicians and theoreticians in the history of mankind. As the foundation for theoretical physics and the associated branches of the engineering sciences, an adequate command of analytical mechanics is an essential tool for any engineer, physicist, and mathematician active in dynamics. A fascinating dis cipline, analytical mechanics is not only indispensable for the solution of certain mechanics problems but also contributes so effectively towards a fundamental under standing of the subject of mechanics and its applications. In analytical mechanics the fundamental laws are expressed in terms of work done and energy exchanged. The extensive use of mathematics is a consequence of the fact that in analytical mechanics problems can be expressed by variational State ments, thus giving rise to the employment of variational methods. Further it can be shown that the independent variables may be either displacements or impulses, thus providing in principle the possibility of two complementary formulations, i.e. a dis placement formulation and an impulse formulation, for each problem. This duality is an important characteristic of mechanics problems and is given special emphasis in the present book.

I — Fundamentals.- II — Differential Variational Formulations.- III — Integral Variational Formulations.- IV — Canonical Transformations and the Hamilton-Jacobi Equation.- V — Rigid Body Dynamics.- VI — Special Applications.- Appendix A — The Calculus of Variations.- A.1 Functions and Functionals.- A.2 Review of Extremum Values of Functions.- A.3 Stationary Values of Definite Integrals.- A.4 A Note about Weak and Strong Variations.- A.5 An Alternative Expression for a Single Euler-Lagrange Equation.- A.6 The Brachystochrone Problem.- A.7 Path-independent Functionals.- A.8 Several Dependent Functions.- A.9 Variational Notation.- A.10 Constraint Equations.- Lagrange Multipliers.- Algebraic and Differential Equation Constraints.- A.11 Variable End Points.- Suggested Reading.- Appendix B — Developments in Mechanics — Some Historical Perspectives.- Author Index.

Reihe/Serie	Solid Mechanics and Its Applications ; 31
Zusatzinfo	XII, 368 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	160 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Technik ► Maschinenbau
ISBN-10	90-481-4422-1 / 9048144221
ISBN-13	978-90-481-4422-8 / 9789048144228
Zustand	Neuware