The equations of motion of multibody systems with holonomic constraints are of index 3 and therefore not directly solvable by standard ODE or DAE methods. Until now, a number of regularization methods have been proposed to treat these systems [1, 2, 3, 4], but as they are based on different points of view they have never been compared with respect to their physical properties, invariance under ...

Using a differential geometric treatment, we analytically derived the expression for De Sitter geodesic precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild’s metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O’Connell 1970, 1975 in a different sett...

We prove the following results: (1) A unique smooth solution exists for short time for the heat equation associated with the MM obius energy of loops in a euclidean space, starting with any simple smooth loop. (2) A critical loop of the energy is smooth if it has cube-integrable curvature. Combining this with an earlier result of M. Freedman, Z. Wang and the author, any local minimizer of the e...

Area-proportional Euler diagrams have many applications, for example they are often used for visualizing data in medical and biological domains. There have been a number of recent research efforts to automatically draw Euler diagrams when the areas of the regions are not considered, leading to a range of different drawing techniques. By contrast, substantially less progress has been made on the...

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conse...

We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is described by fractional integrals. The fractional integrals are considered as approximation of the integrals on fractals. We derive fractional generalization of the...

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.

Let X,Y be Banach modules over a C∗-algebra and let r1, . . . , rn ∈ R be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital C∗-algebra: ∑n j 1 f −rjxj ∑ 1≤i≤n,i / j rixi 2 ∑n i 1 rif xi nf ∑n i 1 rixi . We show that if ∑n i 1 ri / 0, ri, rj / 0 for some 1 ≤ i < j ≤ n and a mapping f : X → Y satisfies the functional equation...

In 1940, Ulam [1] proposed the famous Ulam stability problem of linear mappings. In 1941, Hyers [2] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies Hyers inequality ‖ f (x+ y)− f (x)− f (y)‖ ≤ ε for all x, y ∈ E. It was shown that the limit L(x) = limn→∞ 2−n f (2nx) exists for all x ∈ E and that L : E→ E′ is the unique additive ...