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Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 360))

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Abstract

In this chapter, we study the kinematics, statics and dynamics of isolated rigid bodies, which will find applications in studying the dynamics of multibody systems. With regard to kinematics, morevoer, we study both finite and infinitesimal motions, i.e., motions of a rigid body characterized by both finite and infinitesimal displacements of its points. Hence, we assume a certain level of familiarity with basic point mechanics. Furthermore, we will resort to basic linear algebra and will thus assume that the reader has been exposed to this discipline.

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References

  1. Euler, L. 1776. “Nova methodus motum corporum rigidorum determinandi”, Novii Comentarii Academiæ Scientiarum Petropolitanæ, 20 (1775) 1776: 208–238 = Opera Omnia (2) 9: 99–125.

    Google Scholar 

  2. Halmos, P., 1974, Finite-Dimensional Vector Spaces, Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  3. Cheng, H. and Gupta, K.C., 1989, “An historical note on finite rotations”, ASME Journal of Applied Mechanics, Vol. 56, pp. 139–142.

    Article  MathSciNet  Google Scholar 

  4. Angeles, J. 1982. Spatial Kinematic Chains. Analysis, Synthesis, Optimization, Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  5. Synge, J. L. (1960) “Classical Dynamics”, in Flügge, S. (editor), Encyclopedia of Physics, Vol. III/1, Springer-Verlag, Berlin-Göttingen-Heidelberg: 1–225.

    Google Scholar 

  6. Roth, B., 1984, “Screws, motors, and wrenches that cannot be bought in a hardware store”, in Brady, M. and Pane, R. (editors), Robotics Research. The First International Symposium, the MIT Press, Cambridge (MA), pp. 679–693.

    Google Scholar 

  7. Chasles, M., 1830, “Notes sur les propriétés générales de deux corps semblables entr’eux et placés d’une manière quelconque dans l’espace, et sur le déplacement fini ou infiniment petit d’un corps solide libre”, Bull. Sci. Math. Ferrusaac, Vol. 14, pp. 321–326.

    Google Scholar 

  8. Angeles, I., 1986, “Automatic computation of the screw parameters of rigid-body motions. Part I: Finitely separated positions”, ASME J. of Dynamic Systems. Measurement, and Control, Vol. 108, No. 1, pp. 32–38.

    Article  MATH  Google Scholar 

  9. Bottema, O. and Roth, B., 1990, Theoretical Kinematics, Dover Publications, Mineola, N.Y.

    MATH  Google Scholar 

  10. Angeles, J., 1988, Rational Kinematics, Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  11. Everett, J. D., 1875, “On a new method in statics and kinematics”, Messenger of Mathematics, Vol. 45, pp. 36–37.

    Google Scholar 

  12. Phillips J., 1990, Freedom in Machinery. Vol. 2: Screw Theory Exemplified, Cambridge University Press, Cambridge.

    Google Scholar 

  13. von Mises, R., 1924, “Motorrechnung, ein neues Hilfsmittel der Mechanik”, Z. Angewandte Mathematik und Mechanik, Vol. 4, No. 2, pp. 155–181.

    Article  MATH  Google Scholar 

  14. Coriolis, G. G., 1835, “Mémoire sur les équations du mouvement relatif des systèmes des corps”, J. Ecole Polytechnique, 15, cahier 24: 142–154.

    Google Scholar 

  15. Wang, C.-C., 1979, Mathematical Principles of Mechanics and Electromagnetism. Part A: Analytical and Continuum Mechanics, Plenum Press, New York and London.

    Book  MATH  Google Scholar 

  16. Huston, R. L. and Passerello, C. E., 1974, “On constraint equations—A new approach”, ASME J. Applied Mechanics, Vol. 41, pp. 1130–1131.

    Article  Google Scholar 

  17. Hemami, H. and Weimer, F. C., 1981, “Modeling of nonholonomic dynamic systems with applications”, ASME J. Applied Mechanics, Vol. 48, pp. 177–182.

    Article  MATH  Google Scholar 

  18. Kahaner, D., Moler, C., and Nash, S., 1989, Numerical Methods and Software. Prentice-Hall Inc., Engelwood Cliffs.

    MATH  Google Scholar 

  19. Papastavridis, J. G., 1990, “Maggi’s equations of motion and the determination of constraint reactions”, J. Guidance, Control, and Dynamics, Vol. 13, No. 2, pp. 213–220.

    Article  MATH  MathSciNet  Google Scholar 

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© 1995 Springer-Verlag Wien

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Angeles, J., Kecskeméthy, A. (1995). Fundamentals of Rigid-Body Mechanics. In: Angeles, J., Kecskeméthy, A. (eds) Kinematics and Dynamics of Multi-Body Systems. CISM International Centre for Mechanical Sciences, vol 360. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4362-9_2

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  • DOI: https://doi.org/10.1007/978-3-7091-4362-9_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82731-4

  • Online ISBN: 978-3-7091-4362-9

  • eBook Packages: Springer Book Archive

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