LIOUVILLE’S THEOREM AND THE
FOUNDATION OF CLASSICAL MECHANICS
Andreas Henriksson
Stavanger Katedralskole, Haakon VII’s gate 4, 4005
Stavanger, Norway
Email: andreas.henriksson@skole.rogfk.no
Received 20 January 2022; revised 20 March 2022; accepted 1 April
2022
In this article, it is suggested that a
pedagogical point of departure in the teaching of classical
mechanics is the Liouville’s theorem. The theorem is
interpreted to define the condition that describes the
conservation of information in classical mechanics. The
Hamilton’s equations and the Hamilton’s principle of the least
action are derived from the Liouville’s theorem.
Keywords: information, determinism, Liouville’s
theorem, Hamilton’s equations, Hamilton’s principle
LIUVILIO TEOREMA IR KLASIKINĖS
MECHANIKOS PAGRINDAS
Andreas Henriksson
Stavangerio katedros
mokykla, Stavangeris, Norvegija
References /
Nuorodos
[1] F. Bloch,
Fundamentals of Statistical Mechanics,
Manuscript and Notes of Felix Bloch, prepared by John Dirk
Walecka, 3rd ed. (Imperial College Press and World Scientific
Publishing, London, 2000)
[2] J.W. Gibbs,
Elementary Principles in Statistical
Mechanics (Charles Scribner’s Sons, New York, 1902)
[3] J. Liouville,
Note sur la Theorié de la Variation des
constantes arbitraires, J. Math. Pures Appl.
3(1),
342–349 (1838)
[4] J. Liouville,
Note sur l’intégration des équations
différentielles de la Dynamique, J. Math. Pures Appl.
20(1),
137–138 (1855)
[5] V.I. Arnold,
Mathematical Methods of Classical Mechanics,
2nd ed. (Springer-Verlag, New York, 1989),
https://doi.org/10.1007/978-1-4757-2063-1
[6] H. Jeffreys and B.S. Jeffreys,
Methods of Mathematical
Physics, 3rd ed. (Cambridge University Press, 1956)