La Rivista del Nuovo Cimento (1978-1999)

, Volume 6, Issue 2, pp 1–62

Dynamics and symmetry for constrained systems: a geometrical analysis

  • G. Marmo
  • N. Mukunda
  • J. Samuel

DOI: 10.1007/BF02740487

Cite this article as:
Marmo, G., Mukunda, N. & Samuel, J. Riv. Nuovo Cim. (1983) 6: 1. doi:10.1007/BF02740487



field of real numbers


configuration space

TmQ, Tm*Q

tangent and cotangent spaces at m ε Q

TQ, T * Q

tangent and cotangent bundles of Q

T(Q), X(Q),X * (Q)

algebras of functions, vector fields, 1-forms

TΦ:TQ →TN:TN (Φ [cq])

[Φ o c]Φ(q), where [cq] is the equivalence class of curves tangent at qε Q and ΦQ → N is C∞


exterior derivative


Lie and inner derivative with respect to X ∈ X(Q)


Cartan 1-form on TQ

ω ℒ

d θ ℒ


canonical 2-form on T * Q

in → M

identification map of the submanifold N into M<┐>

Copyright information

© Società Italiana di Fisica 1983

Authors and Affiliations

  • G. Marmo
    • 1
    • 2
  • N. Mukunda
    • 3
  • J. Samuel
    • 4
  1. 1.Sezione di NapoliIstituto Nazionale di Fisica NucleareItalia
  2. 2.Istituto di Fisica Teorica dell’ UniversitàNapoliItalia
  3. 3.Center for Theoretical Studies and Department of PhysicsIndian Institute of ScienceBangaloreIndia
  4. 4.Raman Research InstituteBangaloreIndia