DRAGGING ALONG AND INVARIANT DIFFERENTIATION,
Abstract
A physical system under coherent evolution will usually experience displacements of its constituent mass points, and consequently a description of the fields generated by the mass points must include the effects of these displacements. A method is developed whereby derivatives of general geometric fields can be evaluated at the deformed mass points in terms of quantities evaluated at the original undeformed mass points. A general invariant derivative is defined which has a number of interesting properties in its own right. With this derivative and the Lie difference operator, relations between the dragged along invariant derivative and the invariant derivative of the dragged along field are derived. The point transformations that give rise to the dragging along are considered as finite point transformations, and hence the use of the exponential operator is obviated. Under restriction to infinitesimal deformations, the results reduce to the commutation relations between invariant differentiation and Lie differentiation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1965
- Accession Number
- AD0615946
Entities
People
- Dominic G. B. Edelen
Organizations
- RAND Corporation