The following is slightly modified from the differential geometry part of the book Shape Interrogation for Computer Aided Design and Manufacturing by Nicholas M. Patrikalakis and Takashi Maekawa of MIT. A plane curve can be expressed in parametric form as x = x(t); y = y(t); where the coordinates of the point (x, y) of […]
Let us distinguish between observer-receivers and traveler-transmitters. Although observers can travel and travelers can observe, insofar as one is observing, one is not traveling, and insofar as one is traveling, one is not observing. The main difference is this: traveler-transmitters have a destination but observer-receivers do not (or at least not as observers). Compare the
See also the related post on the Center of vass. Relativity has been addressed before, such as here. Isaac Newton called mass “the quantity of matter”, which is still used sometimes, although Max Jammer points out how it has been criticized for centuries (see Concepts of Mass in Classical and Modern Physics, 1961). Other definitions
One question is how to translate from time rates to space rates and vice versa. Consider the scalars base and time, and designate the stantial position, s, initial stantial position, s0, temporal position, t, initial temporal position, t0, velocity, v, initial velocity, v0, acceleration a (assumed constant over time), lenticity, w, initial lenticity, w0, and
Among the instruments on a vehicle there may be a speedometer, an odometer, a clock, and a compass, which provide scalar (1D) readings of the vehicle’s location. But what is the location of the vehicle in a larger framework? The compass shows two dimensions must exist on a map of this framework, but of what
The 19th century physicist Ernst Mach is known for his view that all motion is relative, which influenced Albert Einstein. Mach is also known for his book The Science of Mechanics (1883 in German, 1893 in translation), from which the following excerpts about physics and theology are taken (Open Court edition, 1960): Consolation, [Pascal] used
We need to distinguish between scalar (1D) and vector (3D) versions of both time and space. Motion in scalar (1D) time and scalar (1D) space is measured by clocks and linear references, respectively, and apply throughout the associated vector space or vector time (in Newtonian mechanics). Scalar time is what a clock measures, which is
I’ve been revising the glossary lately, see above. This required adjusting the post on Foundations of mechanics for time-space, among others. Here is an explanation: Ordinary 3D space is measured by distances. Correspondingly, 3D time is measured by durations. That is, 3D time is a space of times. Call this time space. Ordinary 1D time
This post continues a series of posts. The previous one was here. I’ve noted before that the one-way speed of light is a convention (see John A. Winnie, Philosophy of Science, v. 37, 1970). The two-way (round-trip) speed of light is known to equal c, but the one-way speed may vary between c/2 and infinity,
The measurement of the length of a motion follows the course of motion at its own pace. It is a measurement of something passive, and the motion may be past when the measurement takes place. Cartesian space lacks direction. The independent axes are just coordinates that describe a passive space. The origin is arbitrary and
