On the Dynamics of the Aeroplane and Non-Riemannian Geometry, Part I.

Abstract

Modern concepts in the differential geometry of paths are applied to dynamics especially in the theory of the disturbed motion of an aeroplane. It is pointed out that the combined system of an aeroplane and the surrounding fluid affords a space of affine connection, in which the system behaves as it moves along the path defined by usual non-Riemannian geometry. The coefficients of the aerodynamical forces can be regarded as forming a set of geometric objects which take the role of the parts of the coefficients of affine connection. The equations of small disturbances obtained categorically by the Jacobi criterion for integrability are compared with the usual ones which have been adopted in ordinary technical treatments.Might it be probable that the present treatise would be compared with G. Kron's non-Riemannian dynamics of electrical machinery as its aerodynamical counterpart?