IJPAM: Volume 45, No. 4 (2008)

APPELL'S EQUATIONS AS A COVARIANT FORM
OF THE MOTION EQUATIONS IN
A SUB-SPACE OF RIEMANN'S SPACE

A. Stepniewski
Department of Mathematics
Szczecin University of Technology
Ruska 33c/9, Szczecin, 70-132, POLAND
e-mail: fredstep@poczta.onet.pl


Abstract.In this paper a geometrical interpretation of Appell's equations is provided. For this purpose a 'mass-based' Euclid's multi-dimensional space. This space was arrived at by using the Cartesian product of the sets of the coordinates of points of a material system. In this space, by applying the equations of holonomic constraints, Riemann's multi-dimensional space was introduced. Then, making use of the equations of non-holonomic constraints, a sub-space of Riemann's space was introduced. While Appell's equations are the equations of coordinates, in the covariant form, of the motion equations of a material system in the sub-space of Riemann's space.

Received: April 27, 2008

AMS Subject Classification: 70D05

Key Words and Phrases: Appell's equations, Riemann's space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 45
Issue: 4