Abstract
A rigid body is an idealization of a solid body of finite size in which deformation is neglected. Rigid bodies are characterized as being non-deformable, as opposed to deformable bodies. The distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it. We can use the property that the body is rigid, if all its particles maintain the same distance relative to each other. Therefore it is sufficient to describe the position of at least three non-collinear particles. The rigid body dynamics is the study of the motion of rigid bodies. Unlike point particles, which move only in three degrees of freedom (translation in three directions), rigid bodies occupy a region of space and have spatial properties. The main properties of a rigid body are a center of mass and moments of inertia, that characterize motion in six degrees of freedom such as translations in three directions and rotations in three directions.
This is a preview of subscription content, log in via an institution to check access.
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
A. Carpinteri, P. Cornetti, 2002, A fractional calculus approach to the description of stress and strain localization in fractal media, Chaos, Solitons and Fractals, 13, 85–94.
A. Carpinteri, F. Mainardi (Eds.), 1997, Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York.
R.M. Christensen, 2005, Mechanics of Composite Materials, Dover, New York.
H. Goldstein, C.P. Poole, J.L. Safko, 2002, Classical Mechanics, 3nd ed., Addison-Wesley, San Fransisco.
V.S. Ivanova, A.S. Balankin, I.Zh. Bunin, A.A. Oksogoev, 1994, Synergetics and Fractals in Material Sciences, Nauka, Moscow. In Russian.
A.A. Kubas, H.M. Srivastava, J.J. Trujillo, 2006, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
M.I. Kulak, 2002, Fractal Mechanics of Materials, Visheishaya Shkola, Minsk. In Russian.
F. Mainardi, 2010, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, World Scientific Publishing, Singapore.
Y. Park, 2000, On fractal theory for porous media, Journal of Statistical Physics, 101, 987–998.
F.Y. Ren, J.R. Liang, X.T. Wang, W.Y. Qiu, 2003, Integrals and derivatives on net fractals, Chaos, Solitons and Fractals, 16, 107–117.
S.G. Samko, A.A. Kubas, O.I. Marichev, 1993, Integrals and Derivatives of Fractional Order and Applications, Nauka i Tehnika, Minsk, 1987, in Russian; andand Fractional Integrals and Derivatives Theory and Applications, Gordon and Breach, New York, 1993.
Special Issue, 1997, Application of Fractals in Material Science and Engineering, Chaos, Solitons and Fractals, 8, 135–301.
V.E. Tarasov, 2004, Fractional generalization of Liouville equations, Chaos 14, 123–127.
V.E. Tarasov, 2005a, Continuous medium model for fractal media, Physics Letters A, 336, 161–114.
V.E. Tarasov, 2005b, Fractional hydrodynamic equations for fractal media, Annals of Physics, 318, 286–307.
V.E. Tarasov, 2005c, Fractional systems and fractional Bogoliubov hierarchy equations, Physical Review E, 71, 011102.
V.E. Tarasov, 2005d, Dynamics of fractal solid, International Journal of Modern Physics B, 19, 4103–4114.
V.E. Tarasov, 2005e, Possible experimental test of continuous medium model for fractal media, Physics Letters A, 341, 467–472.
V.E. Tarasov, 2005f, Wave equation for fractal solid string, Modern Physics Letters B, 19, 721–728.
V.E. Tarasov, 2005g, Fractional Liouville and BBGKI equations, Journal of Physics: Conference Series, 7, 17–33.
K. Tsujii, 2008, Fractal materials and their functional properties, Polymer Journal, 40, 785–799.
V.V. Uchaikin, 2008, Method of Fractional Derivatives, Artishok, Ulyanovsk. In Russian.
G.V. Vostovsky, A.G. Kolmakov, I.Zh. Bunin, 2001, Introduction to Multifractal Parametrization of Material Structure, RHD, Moscow. In Russian.
I.V. Zolotuhin, Yu.E. Kalinin, V.I. Loginova, 2005, Solid fractal structures, International Scientific Journal for Alternative Energy and Ecology, 9, 56–66.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2010 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tarasov, V.E. (2010). Fractal Rigid Body Dynamics. In: Fractional Dynamics. Nonlinear Physical Science, vol 0. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14003-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-14003-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14002-0
Online ISBN: 978-3-642-14003-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)