Abstract
Kinematics is the study of position, velocity and acceleration without the need of forces. Kinematics, however, for years used kinematical relations to design linkages, gears and a number of complex engineering problems. Although in principle we can analyze the motion of a system of N degrees of freedom, we often rely on simple models to obtain realistic answers. The concept of a rigid body is a good example where we assume that the body doesn’t deform under the influence of external forces or simply the deformation is negligible. In this chapter, we set the foundation for the kinematical quantities needed to describe a rigid-body motion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Coyley, A., On the Rotation of a Solid Body Round a Fixed Point. Cambridge Dublin Math J., Vol. I, 1846, pp. 167–173; also Collect. Math. Pap., Vol. I (Paper 37), Cambridge University Press, 1889, pp. 237–252.
Gibbs, J. W., in Vector Analysis (E. B. Wilson, ed.), Scribners, New York, 1901, and Yale University Press, New Haven, Conn., 1931.
Hamel, G., Theoretische Mechanik, Springer-Verlag, Berlin, 1949.
Euler, L., Formulae Generates pro Translatione Quawnque Corporum Rigidorum, Novi Commentari Acad. Imp. Petrop. 20, 1775, pp. 189–207.
Euler, L., Nova Methodus Motum Corporum Rigidorum determinandi, Novi Commentari Acad. Imp. Petrop. 20, 1775, pp. 208–238.
Goldstein, H., Classical Mechanics, Addison-Wesley, Reading, MA, 1980.
Kane, T. R., Likins, P. W. and Levinson, D. A., Spacecraft Dynamics, McGraw-Hill, New York, 1983.
Rodriguez, O., Des lois géométriques qui régissent les déplacements d’un system solide dans l’espace, et la variation des coordonnées provenant des déplacements considéres indépendamment des causes qui peuvent les produire, J. Math. Pures Appl., Vol. 5, 1840, pp. 380–440.
Wittaker, E. T., Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, Cambridge, 1937 (first edition, 1904).
Cheng, H. and Gupta, K. C., A Historical Note on Finite Rotations, J. Appl. Mech. Vol. 56: No. 1, 1989, pp. 139–145.
Ginsberg, J. H., Advanced Engineering Dynamics, Harper & Row, New York, 1988.
Kane, T. R. and Levinson, D. A., Dynamics: Theory and Applications, McGraw-Hill, New York, 1985.
Paul, B., On the Composition of Finite Rotations, Am. Math. Mon., Vol. 70, 1963, pp. 949–954.
Hill, E. L., Rotation of a Rigid Body About a Fixed Point, Am. J. Phys., Vol. 13, 1945, 137–140.
Beatty, M. F., Vector Analysis of Finite Rigid Rotations, Trans. ASME J. Appl. Mech., Vol. 44, 1977, pp. 501–502.
Meriovitch, L., Methods of Analytical Dynamics, McGraw-Hill, New York, 1970.
Ronald L. Huston, Multibody Dynamics, Butterworth-Heinemann, 1990.
Rights and permissions
Copyright information
© 2006 Birkhäuser Boston
About this chapter
Cite this chapter
(2006). Rigid-Body Kinematics. In: Fundamentals of Multibody Dynamics. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4406-7_2
Download citation
DOI: https://doi.org/10.1007/0-8176-4406-7_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4236-5
Online ISBN: 978-0-8176-4406-2
eBook Packages: EngineeringEngineering (R0)