Abstract In this technical brief, a simple concise derivation of the Gibbs-Appell equations for dynamics constrained rigid body is presented.

This paper develops an extended form of the Gibbs-Appell equation and shows that it is equivalent to the generalized inverse equation of motion. Both equations are shown to follow from Gauss's principle. An example to highlight the two equivalent, though different, equations of motion is provided. Conceptual differences between the equations, and differences in their practical application to ph...

A method for solving the complete dynamic problem in robots with rigid links and ideal joints using the Gibbs–Appell equations as starting point is presented. The inverse dynamic problem is solved through a algorithm OðnÞ, where tensor notation is used. The terms of the generalized inertia matrix are calculated by means of the Hessian of the Gibbs function with respect to generalized accelerati...

The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Four...

In the last years the Appell polynomials, named after Paul Émile Appell which introduced them in 1880 [1], have gained renewed interest and has been studied by several authors. In particular, some new characterizations of Appell polynomials themselves through new approaches have been considered. To quote some of them we mention, for instance, the novel approach developed in [5], which makes use...