Speed is the length of travel per unit of duration (or time interval). Spatial rest is a speed of zero. That is, there is no change in location per unit of time. A body does not change location (relative to an inertial observer) while time continues. But temporal rest seems different. It cannot be zero […]
The following is based on A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekeres (Cambridge UP, 2004) starting with Example 2.29 on page 54 and modifying it for a temporo-spatial context. The Galilean group. To find the set of transformations of space and time that preserve the laws of
The following is a temporo-spatial modification of the book Mechanics, Third Edition, Volume I of Course of Theoretical Physics by L. D. Landau and E. M. Lifshitz, (Butterworth-Heinenann, Oxford, 1976). [Page 1] §1. CHAPTER I – THE EQUATIONS OF MOTION §1. Generalised co-ordinates ONE of the fundamental concepts of mechanics is that of a particle¹.
Extracts about Galileo from Scientific Method: An historical and philosophical introduction by Barry Gower (Routledge, 1997): Galileo took great pains to ensure that his readers would be persuaded that his conclusions were correct. p. 23 The science of motion was then understood to be a study of the causes of motion, and to be, like
The following derivation of the Lorentz transformation is slightly revised from the Appendix to Henri Poincaré: a decisive contribution to Relativity by Christian Marchal, originally published in French as Henri Poincaré: une contribution décisive à la Relativité in La Jaune et la Rouge, août-septembre 1999. Marchal is the chief engineer of mines at ONERA, the Office
A clock consists of two frames of reference. This is seen in an ordinary analogue clock, which is composed of two parts: The space frame is at rest relative to the observer. The time frame is in uniform angular motion relative to the observer. Measurement of space and time requires both frames. The units marked
V. I. Arnold’s Mathematical Methods of Classical Mechanics (Springer, 1989) provides a contemporary approach to classical mechanics. We follow the presentation here but modify it to six dimensions of space-time. 1 The principles of relativity and determinacy A series of experimental facts is at the basis of classical mechanics. We list some of them. A
Four-Dimensional Formulations of Newtonian Mechanics First we reproduce section 2 from Michael Friedman’s “Simultaneity in Newtonian Mechanics and Special Relativity” in Foundations of Space-Time Theories (ed. Earman et al., UMinn, 1977), p.405-407. Then we provide the dual. According to the spatio-temporal point of view, the basic object of both our theories is a four-dimensional manifold.
We follow the treatment by David Tong of Cambridge University in his Classical Dynamics. A tempicle is defined as a moving object of insignificant time. The motion of a tempicle of vass n at the chronation t is governed by Newton’s Distance Domain Second Law, R = nb or, more precisely, R(t; t′) = h′
This is an update and expansion of the post here. Here is a derivation of the chorocosmic equations of motion, in which acceleration is constant. Let time = t, location = x, initial location = x(t0) = x0, velocity = v, initial velocity = v(t0) = v0, speed = v = |v|, and acceleration =
