Seminar

We suggest a mathematical tool for the kinematics of higher order accelerations. The tool is equipped with Riccati and Appell differential equations, Pascal matrices and elements of the generalized trigonometry. Evolution equations for the coefficients of the polynomials are derived. These equations are generated by exponential functions of the nilpotent matrices. The polynoials form the Appell sequences. The first example, the jerk kinematics, is described by the third degree polynomial of time which is formed under action of the shifts of three points on the axis of time. In general, the number of points is equal to the degree of the pivot polinomial. Under a special choose of the initial data the set of polynomials describing the higher order accelerations are reduced to the set of Hermite polynomials. The method is quite general and can be applied in different models of mathematical physics.