38 citations · 281 across the 52 of their papers we have counts for
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Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Dmitry Lyakhov, Vladimir Gerdt, Andreas Weber +1
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechan…
On the General Analytical Solution of the Kinematic Cosserat Equations
Dominik Michels, Dmitry Lyakhov, Vladimir Gerdt +3
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of e…
On the Partial Analytical Solution of the Kirchhoff Equation
Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt +2
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient…
Lie Symmetry Analysis for Cosserat Rods
Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt +2
We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary…
Completion of Linear Differential Systems to Involution
Vladimir P. Gerdt
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in…