La Rivista del Nuovo Cimento (1978-1999)

, Volume 6, Issue 2, pp 1–62 | Cite as

Dynamics and symmetry for constrained systems: a geometrical analysis

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

Notation

R

field of real numbers

Q

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∞

d

exterior derivative

Lx,ix

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

θ

Cartan 1-form on TQ

ω ℒ

d θ ℒ

ω0

canonical 2-form on T * Q

in → M

identification map of the submanifold N into M<┐>

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References

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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

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