Kinematic and geometrical aspects of the connection between energy and inertial mass are considered. Transformations of coordinate and time are obtained in a two-dimensional flat space. For this case the Euclidean, pseudo-Euclidean and Galilean kinematics are considered. A new interval in a flat fourdimensional anisotropic Finsler space is found. Under certain assumptions the known results foll...

It is widely accepted that the notion of inertial frame is central to Newtonian mechanics, and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parall...

We present the basic concepts of space and time, Galilean pseudo-Euclidean geometry. use an elementary geometric framework affine spaces groups transformations to illustrate natural relationship between classical mechanics theory relativity, which is quite often hidden, despite its fundamental importance. have emphasized a passage from group motions Poincaré plane. In particular, 1-parametric f...

The failure of Maxwell's equations to exhibit invariance under the Galilean transformation was corrected by Hertz through a simple, but today largely forgotten, mathematical trick. This involves substituting total (convective) time derivatives for partial time derivatives wherever the latter appear in Maxwell's equations. By this means Hertz derived a formally Galilean-invariant covering theory...

We study the so-called factorable surfaces in pseudo-Galilean space, graphs of product two functions one variable. then classify these when mean and Gaussian curvatures are

A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be “velocity adapted”, i.e. to have Galilean covariance to avoid favoring any particular motion. Furthermore standard scale-space axioms: linearity, positivity, continuity, translation invariance, scaling covari...