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Unformatted text preview: 1 Newton’s Second Law
The form of Newton’s second law for three separate cases will be generated using quaternion operators acting on position quaternions. In classical mechanics, time and space are decoupled. One way that can be achieved algebraically is by having a time operator cat only on space, or by space operator only act on a scalar function. I call this the ”2 zero” rule: if there are two zeros in the generator of a law in physics, the law is classical. Newton’s 2nd Law for an Inertial Reference Frame in Cartesian Coordinates
Deﬁne a position quaternion as a function of time.
R t, R Operate on this once with the differential operator to get the velocity quaternion.
V t, R Operate on the velocity to get the classical inertial acceleration quaternion.
A This is the standard form for acceleration in Newton’s second law in an inertial reference frame. Because the reference frame is inertial, the ﬁrst term is zero. Newton’s 2nd Law in Polar Coordinates for a Central Force in a Plane
Repeat this process, but this time start w...
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- Spring '10