As a result the upper vertical position, which is unstable in a mathematical pendulum, can become stable in Kapitza's pendulum.

The total energy is conserved in a mathematical pendulum, so time dependence of the potential and kinetic energies is symmetric with respect to the horizontal line.

The first minimum is in the same position as the mathematical pendulum and the other minimum is in the upper vertical position .

Huygens was the first to derive the formula for the period of an ideal mathematical pendulum (with massless rod or cord and length much longer than its swing), in modern notation:

Such a pendulum may be called a "simple" pendulum; the enclosure of the word simple by quotation marks is to indicate that such a pendulum is an approximation to a simple, or mathematical pendulum, a conceptual object which consists of a mass-point suspended by a weightless inextensible cord.