非ホロノミック・不等式拘束力学への変分アプローチ
Variational approach to nonholonomic and inequality-constrained mechanics
非可積分な速度拘束や位置の不等式拘束を受ける系に対し、シュウィンガー＝ケルディッシュ作用の古典極限に着想を得た明示的な作用を構成し、その極値化からラグランジュ＝ダランベール方程式を再現できることを示した。
著者: A. Rothkopf, W. A. Horowitz
分類: physics.class-ph, cs.RO, math-ph, math.MP
原文アブストラクト
Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems -- subject to non-integrable velocity constraints or position inequality constraints -- have long resisted a general extremized action treatment. In this work, we construct an explicit and general action for non-holonomic motion, motivated by the classical limit of the quantum Schwinger-Keldysh action formalism, rediscovered by Galley. Our formulation recovers the correct dynamics of the Lagrange-d'Alembert equations via extremization of a scalar action. We validate the approach on canonical examples using direct numerical optimization of the novel action, bypassing equations of motion. Our framework extends the reach of variational mechanics and offers new analytical and computational tools for constrained systems.