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On the multisymplectic formalism for first order field theories
- J. Cariñena, M. Crampin, L. A. Ibort
- Mathematics
- 1 December 1991
Applicable Differential Geometry
- M. Crampin, F. Pirani
- Mathematics
- 24 April 1987
The background: vector calculus 1. Affine spaces 2. Curves, functions and derivatives 3. Vector fields and flows 4. Volumes and subspaces: exterior algebra 5. Calculus of forms 6. Frobenius's theorem…
A geometrical version of the Helmholtz conditions in time- dependent Lagrangian dynamics
- M. Crampin, G. Prince, G. Thompson
- Mathematics
- 11 May 1984
Appropriate geometrical machinery for the study of time-dependent Lagrangian dynamics is developed. It is applied to the inverse problem of the calculus of variations, and a set of necessary and…
Higher-order differential equations and higher-order lagrangian mechanics
- M. Crampin, W. Sarlet, F. Cantrijn
- Mathematics
- 1 May 1986
On considere le role du champ d'equation differentielle d'ordre eleve Γ qui definit la dynamique. C'est un champ vectoriel sur T N M. On etudie la methode pour definir un lagrangien
On the Legendre map in higher-order field theories
- D. Saunders, M. Crampin
- Mathematics
- 21 July 1990
The authors show how the construction of a Cartan form in higher-order field theories defines a Legendre map, and how the regularity of this map may be described in terms of a sequence of maps…
The Hilbert-Caratheodory and Poincare-Cartan forms for higher-order multiple-integral variational problems
- M. Crampin, D. Saunders
- Mathematics
- 2004
We consider higher-order homogeneous multiple-integral variational problems defined in the context of m-frame bundles, and construct an m-form (the Hilbert-Caratheodory form) with the same extremals…
Cartan Geometries and their Symmetries: A Lie Algebroid Approach
- M. Crampin, D. Saunders
- Mathematics
- 21 May 2016
In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the…
The multiplier approach to the projective Finsler metrizability problem
- M. Crampin, T. Mestdag, D. Saunders
- Mathematics
- 14 March 2012
Tangent bundle geometry Lagrangian dynamics
- M. Crampin
- Mathematics
- 11 November 1983
Various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined, and the results applied to time-independent Lagrangian dynamics. It is shown that a…
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