Abstract The equations of motion for the simplest non-holonomically constrained system particles are formulated using six methods: Newton–Euler, Lagrange, Maggi, Gibbs–Appell, Kane, and Boltzmann–Hamel. challenging tasks exploring explaining relationships equivalences between these formulations is accomplished by constructing a single representative particle particles. to move on configuration ...

This paper deals with the identification problem of the inertial and frictional parameters of a parallel manipulator. Two important issue are considered; the physical feasibility of the identified inertial parameters and the use of linear and nonlinear friction models. The dynamic model, analyzed and reduced to a set of base parameters through the Singular Value Decomposition, is derived starti...

In SU(2) Seiberg-Witten theory, it is known that the dual pair of fields are expressed by hypergeometric functions. As for the theory with SU(3) gauge symmetry without matters, it was shown that the dual pairs of fields can be expressed by means of the Appell function of type F4. These expressions are convenient for analyzing analytic properties of fields. We investigate the relation between Se...

Appell systems can be interpreted as polynomial solutions of generalized heat equations, and in probability theory they have been used to obtain non-central limit theorems. The natural grade-decomposition of a Clifford algebra of arbitrary signature lends it a natural Appell system decomposition. Motivated by evolution equations on Clifford algebras, combinatorial raising and lowering operators...

A Laguerre polynomial sequence of parameter ε/2 was previously characterized in a recent work [Ana F. Loureiro and P. Maroni (2008) [28]] as an orthogonal Fε-Appell sequence, where Fε represents a lowering (or annihilating) operator depending on the complex parameter ε ≠ −2n for any integer n ⩾ 0. Here, we proceed to the quadratic decomposition of anFε-Appell sequence, and we conclude that the ...

This paper aimed to study the behavior of a body (dummy) that was in race car event frontal collision with wall order see what loads were acting on dummy. Based complex model, equipped two safety system seat belts and shock absorption system, dummy obtained following car–dummy assembly. The accelerations at different points dummy’s force appeared determined. Gibbs–Appell method used assess resp...

The lateral instabilities of vehicles are well-known phenomena, see for example, the shimmy motions of bikes, motorbikes or the steered wheels of cars. Another interesting phenomenon is the snaking motion of the skateboard-skater system that is analyzed in this study. A mechanical model of the downhill skateboarding is constructed in order to consider the effect of the slope angle on the stabil...

In this article, a new systematic method for deriving the dynamic equations of motion for exible robotic manipulators is developed by using the Gibbs-Appell assumed modes method. The proposed method can be applied to the dynamic simulation and control system design of exible robotic manipulators. In the proposed method, the link de ection is described by a truncated modal expansion. All the mat...

We suggest an approximation for the zero-balanced Appell hyper-geometric function F 1 near the singular point (1, 1). Our approximation can be viewed as a generalization of Ramanujan's approximation for zero-balanced 2 F 1 and is expressed in terms of 3 F 2. We find an error bound and prove some basic properties of the suggested approximation which reproduce the similar properties of the Appell...

This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...