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The vector r from the origin to the current position. It is also called the position vector. The derivative of r satisfies ...

The composition quotient groups belonging to two composition series of a finite group G are, apart from their sequence, isomorphic in pairs. In other words, if I subset H_s ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

The angular acceleration alpha is defined as the time derivative of the angular velocity omega, alpha=(domega)/(dt)=(d^2theta)/(dt^2)z^^=(a)/r.

Let the nth composition of a function f(x) be denoted f^((n))(x), such that f^((0))(x)=x and f^((1))(x)=f(x). Denote the composition of f and g by f degreesg(x)=f(g(x)), and ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

The length of all composition series of a module M. According to the Jordan-Hölder theorem for modules, if M has any composition series, then all such series are equivalent. ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

The jerk j is defined as the time derivative of the vector acceleration a, j=(da)/(dt).

A composition of a function f degreesf with itself gives a nested function f(f(x)), f degreesf degreesf which gives f(f(f(x)), etc. Function nesting is implemented in the ...