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Given a simple harmonic oscillator with a quadratic perturbation, write the perturbation term in the form alphaepsilonx^2, x^..+omega_0^2x-alphaepsilonx^2=0, (1) find the ...

The angular velocity omega is the time derivative of the angular distance theta with direction z^^ perpendicular to the plane of angular motion, omega=(dtheta)/(dt)z^^=(v)/r.

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

Also known as Kolmogorov entropy, Kolmogorov-Sinai entropy, or KS entropy. The metric entropy is 0 for nonchaotic motion and >0 for chaotic motion.

Any motion of a rigid body in space at every instant is a screw motion. This theorem was proved by Mozzi and Cauchy.

A linkage used in the original steam engine to turn back-and-forth motion into approximately straight-line motion.

A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, ...

The three circular triangles A^'B^'C^', AB^'C^', A^'BC^', and A^'B^'C obtained by extending the arcs of a circular triangle ABC into complete circles.

An integral of motion which restricts the phase space available to a dynamical system.

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.