8 citations · 11 across the 11 of their papers we have counts for
16 papers
Maximal Multiplicity Method for Optimal Damping Problem
Maxim Arnold, Oleg Gendelman, Vadim Zharnitsky
We study the problem of designing optimal damping for a system of coupled linear oscillators. Using the Weyl--Horn theorem, we construct an explicit damping matrix that realize…
Critical damping in linear system with two degrees of freedom: surprises and pitfalls
Maxim D. Arnold, Oleg V. Gendelman, Vadim Zharnitsky
In this Brief Communication, we establish the notion of critical damping for generic two-degree-of-freedom system. For given set of masses and stiffnesses, the critical damping cor…
On projective evolutes of polygons
Maxim Arnold, Richard Evan Schwartz, Serge Tabachnikov
The evolute of a curve is the envelope of its normals. In this note we consider a projectively natural discrete analog of this construction: we define projective perpendicular bise…
Topological invariants of sorting networks
Maxim Arnold, Christian Kondor
In this note we investigate finite-type invariants of the pure braids arising from signed sorting networks.
Remarks on Joachimsthal integral and Poritsky property
Maxim Arnold, Serge Tabachnikov
The billiard in an ellipse has an integral linear in momentum, the Joachimsthal integral. We show that the existence of such an integral characterizes conics. We extend this result…
Cross-ratio dynamics on ideal polygons
Maxim Arnold, Dmitry Fuchs, Ivan Izmestiev +1
Two ideal polygons, and , in the hyperbolic plane or in hyperbolic space are said to be -related if the cross-ratio $[p_i,p_{i+1},q_i,q_{i+1…