Dynamics of a Material Point

  • Antonio Romano
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


A positional force is said to be central with center O if its force law is
$$\mathbf{F} = f(r)\frac{\mathbf{r}} {r},\quad r = \vert \mathbf{r}\vert,$$
where r is the position vector relative to O.


Phase Portrait Material Point Inertial Frame Elliptic Orbit Central Force 


  1. 1.
    Abraham, R., Marsden, J.E.: Foundation of Mechanics. Benjamin Cummings, Reading, Mass. (1978)Google Scholar
  2. 2.
    Arnold, V.L.: Equazioni Differenziali Ordinarie. Mir, Moscow (1979)Google Scholar
  3. 3.
    Arnold, V.L.: Metodi Matematici della Meccanica Classica. Editori Riuniti, Rome (1979)MATHGoogle Scholar
  4. 4.
    Barger, V., Olsson, M.: Classical Mechanics: A Modern Perspective. McGraw-Hill, New York (1995)Google Scholar
  5. 5.
    Bellomo, N., Preziosi, L., Romano, A.: Mechanics and Dynamical Systems with Mathematica. Birkhäuser, Basel (2000)MATHCrossRefGoogle Scholar
  6. 6.
    Birkhoff, G., Rota, G.C.: Ordinary Differential Equations. Wiley, New York (1989)Google Scholar
  7. 7.
    Bishop, R.L., Goldberg, S.I.: Tensor Analysis on Manifolds. MacMillan, New York (1968)MATHGoogle Scholar
  8. 8.
    Boothby, W.M.: An Introduction to Differential Manifolds and Riemannian Geometry. Academic, San Diego (1975)Google Scholar
  9. 9.
    Borrelli, R.L., Coleman, C.S.: Differential Equations: A Modeling Approach. Prentice-Hall, Englewood Cliffs, NJ (1987)Google Scholar
  10. 10.
    Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Diluite gases. Springer, Berlin Heidelberg New York (1994)Google Scholar
  11. 11.
    Choquet-Bruhat, Y.: Gèometrie Diffèrentielle et Systèmes Extèrieurs. Dunod, Paris (1968)MATHGoogle Scholar
  12. 12.
    Chow, T.L.: Classical Mechanics. Wiley, New York (1995)Google Scholar
  13. 13.
    Crampin, M., Pirani, F.: Applicable Differential Geometry. Cambridge University Press, Cambridge (1968)Google Scholar
  14. 14.
    de Carmo, Manfredo P.: Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, NJ (1976)Google Scholar
  15. 15.
    Dixon, W.G.: Special Relativity: The Foundations of Macroscopic Physics. Cambridge University Press, Cambridge (1978)Google Scholar
  16. 16.
    Dubrovin, B.A., Novikov, S.P., Fomenko, A.T.: Geometria delle Superfici, dei Gruppi di Trasformazioni e dei Campi. Editori Riuniti, Rome (1987)Google Scholar
  17. 17.
    Dubrovin, B.A., Novikov, S.P., Fomenko, A.T.: Geometria e Topologia delle Varietà. Editori Riuniti, Rome (1988)Google Scholar
  18. 18.
    Dubrovin, B.A., Novikov, S.P., Fomenko, A.T.: Geometria Contemporanea. Editori Riuniti, Rome (1989)Google Scholar
  19. 19.
    Fasano, A., Marmi, S.: Meccanica Analitica. Bollati Boringhieri, Turin (1994)Google Scholar
  20. 20.
    Fawles, G., Cassidy, G.: Analytical Dynamics. Saunders, Ft. Worth, TX (1999)Google Scholar
  21. 21.
    Flanders, H.: Differential Forms with Applications to the Physical Sciences. Academic, New York (1963)MATHGoogle Scholar
  22. 22.
    Fock, V.: The Theory of Space, Time and Gravitation, 2nd edn. Pergamon, Oxford (1964)Google Scholar
  23. 23.
    Goldstein, H.: Classical Mechanics, 2nd edn. Addison-Wesley, Reading, MA (1981)Google Scholar
  24. 24.
    Goldstein, H., Poole, C., Safko, J.: Classical Mechanics, 3rd edn. Addison Wesley, Reading, MA (2002)Google Scholar
  25. 25.
    Hale, J., Koçak, H.: Dynamics and Bifurcations. Springer, Berlin Heidelberg New York (1991)MATHCrossRefGoogle Scholar
  26. 26.
    Hill, R.: Principles of Dynamics. Pergamon, Oxford (1964)MATHGoogle Scholar
  27. 27.
    Hutter, K., van der Ven, A.A., Ursescu, A.: Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids. Springer, Berlin Heidelberg New York (2006)Google Scholar
  28. 28.
    Jackson, E.A.: Perspectives of Nonlinear Dynamic, vol. I. Cambrige University Press, Cambridge (1990)CrossRefGoogle Scholar
  29. 29.
    Jackson, E.A:, Perspectives of Nonlinear Dynamic, vol. II. Cambrige University Press, Cambridge (1990)Google Scholar
  30. 30.
    Josè, J.V., Saletan, E.: Classical Dynamics: A Contemporary Approach. Cambridge University Press, Cambridge (1998)MATHCrossRefGoogle Scholar
  31. 31.
    Khinchin, A.I.: Mathematical Foundations of Statistical Mechanics. Dover, New York (1949)MATHGoogle Scholar
  32. 32.
    Landau, L., Lifshitz, E.: Mechanics, 3rd edn. Pergamon, Oxford (1976)Google Scholar
  33. 33.
    MacMillan, W.D.: Dynamics of Rigid Bodies. Dover, New York (1936)MATHGoogle Scholar
  34. 34.
    Marasco, A.: Lindstedt-Poincarè method and mathematica applied to the motion of a solid with a fixed point. Int. J. Comput. Math. Appl. 40, 333 (2000)MATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    Marasco, A., Romano, A.: Scientific Computing with Mathematica. Birkhauser, Basel (2001)MATHCrossRefGoogle Scholar
  36. 36.
    Möller, C.: The Theory of Relativity, 2nd edn. Clarendon, Gloucestershire, UK (1972)Google Scholar
  37. 37.
    Norton, J.D.: General covariance and the foundations of general relativity: eight decades of dispute. Rep. Prog. Phys. 56, 791–858 (1993)CrossRefMathSciNetGoogle Scholar
  38. 38.
    Panowsky, W., Phyllips, M.: Classical Electricity and Magnetism. Addison-Wesley, Reading, MA (1962)Google Scholar
  39. 39.
    Penfield, P., Haus, H.: Electrodynamics of Moving Media. MIT Press, Cambridge, MA (1967)Google Scholar
  40. 40.
    Petrovski, I.G.: Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs, NJ (1966)MATHGoogle Scholar
  41. 41.
    Resnick, R.: Introduction to Special Relativity. Wiley, New York (1971)Google Scholar
  42. 42.
    Rindler, W.: Introduction to Special Relativity. Clarendon Press, Gloucestershire, UK (1991)MATHGoogle Scholar
  43. 43.
    Romano, A., Lancellotta, R., Marasco, A.: Continuum Mechanics using Mathematica, Fundamentals, Applications, and Scientific Computing. Birkhauser, Basel (2006)MATHGoogle Scholar
  44. 44.
    Romano, A., Marasco, A.: Continuum Mechanics, Advanced Topics and Research Trends. Birkhauser, Basel (2010)MATHCrossRefGoogle Scholar
  45. 45.
    Saletan, E.J., Cromer, A.H.: Theoretical Mechanics. Wiley, New York (1971)MATHGoogle Scholar
  46. 46.
    Scheck, F.: Mechanics: From Newton’s Laws to Deterministic Chaos. Springer, Berlin Heidelberg New York (1990)Google Scholar
  47. 47.
    Stratton, J.A.: Electromagnetic Theory. McGraw-Hill, New York (1952)Google Scholar
  48. 48.
    Synge, J.: Relativity: The Special Theory, 2nd edn. North-Holland, Amsterdam (1964) (Reprint 1972)Google Scholar
  49. 49.
    Synge, J.L., Griffith, B.A.: Principles of Mechanics. McGraw-Hill, New York (1959)Google Scholar
  50. 50.
    Thomson, C.J.: Mathematical Statistical Mechanics. Princeton University Press, Princeton, NJ (1972)Google Scholar
  51. 51.
    Truesdell, C., Noll, W.: The Nonlinear Field Theories of Mechanics. Handbuch der Physik, vol. III/3. Springer, Berlin Heidelberg New York (1965)Google Scholar
  52. 52.
    von Westenholz, C.: Differential Forms in Mathematical Physics. North-Holland, New York (1981)Google Scholar
  53. 53.
    Wang, K.: Statistical Mechanics, 2nd edn. Wiley, New York (1987)Google Scholar
  54. 54.
    Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press, Cambridge (1989)Google Scholar
  55. 55.
    Zhang, W-B.: Differential Equations, Bifurcations, and Chaos in Economy. World Scientific, Singapore (2005)Google Scholar
  56. 56.
    Zhong Zhang, Y.: Special Relativity and Its Experimental Foundations. Advanced Series on Theoretical Physical Science, vol. 4. World Scientific, Singapore (1997)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Antonio Romano
    • 1
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di NapoliNapoliItalia

Personalised recommendations