Modelling of rotations by using matrix solutions of nonlinear wave equations

Abstract

A family of matrix solutions of nonlinear wave equations is extended and its application to modelling is given. It is shown that a similarity transformation, induced by the matrix solution, is equivalent to the rotation. Matrix solutions are used for modelling helical motions and vortex rings, simultaneous rotations and particles collision, mapping contraction and pulsating spheres. Geometrical interpretation of the doubling of rotation angle in each step of sequential mapping contraction is given.

Key words:

• anti‐commuting matrices
• mapping contraction
• matrix solution
• nonlinear wave equation
• particles collision
• rotation
• vortex ring