The Journal of the Indian Mathematical Society

K. Nagabhushanam

Abstract

It is well-known that the field due to a magnetic shell at a point outside it is capable of a two-fold representation, viz., (l) as the negative of the gradient of a scalar potential Ψ and (2) as the curl of a vector potential (P_i).

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K. Nagabhushanam ¹

Affiliations
1 Andhra University, IN

Abstract

In affine manifold of states and time A_2n+1, we have the following facts.

1. The trajectories of a dynamical system with n degrees of freedom are given by the singular curves of the curl of (X_i).

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K. Nagabhushanam ¹

Affiliations
1 Andhra University, Waltair, IN

Abstract

When the Hamiltonian is independent of time, the solution of the dynamical problem can be reduced to depend on that of another system whose number of degrees of freedom is one less than that of the original system.

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K. Nagabhushanam ¹

Affiliations
1 Andhra University, Waltair, IN

Abstract

In a previous paper I have defined the notions of time, the Hamiltonian and the Lagrangian for a given time measure in terms of a Pfaffian X_idxⁱ of class 2n+l in the 2n+1 variables of the manifold of states and time, representing the action of a dynamical system in an infinitesimal displacement. Adopting the the same point of view, I here derive invariant expressions for the kinetic and the potential energies of the system by restricting the admitted transformations to the projective subgroup of the general analytic transformations.

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