Abstract:
This paper addresses the dynamics of systems with servoconstraints where the constraints are realized by controlling the inertial properties of the system. Vakonomic systems are a particular case. Special attention is given to the motion on Lie groups with left-invariant kinetic energy and a left-invariant constraint. The presence of symmetries allows the dynamical equations to be reduced to a closed system of differential equations with quadratic right-hand sides. As the main example, we consider the rotation of a rigid body with a left-invariant servo-constraint, which implies that the projection of the body’s angular velocity on some body-fixed direction is zero.
Keywords:
servoconstraints, symmetries, Lie groups, left-invariant constraints, systems with quadratic right-hand sides, vakonomic systems.
Citation:
V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, Nelin. Dinam., 11:3 (2015), 579–611; Regular and Chaotic Dinamics, 20:4 (2015), 401–427
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G. K. Tolokonnikov, Lecture Notes on Data Engineering and Communications Technologies, 158, Advances in Intelligent Systems, Computer Science and Digital Economics IV, 2023, 126
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E. A. Mikishanina, “Rolling motion dynamics of a spherical robot with a pendulum actuator controlled by the Bilimovich servo-constraint”, Theoret. and Math. Phys., 211:2 (2022), 679–691
Kahramanjon Khusanov, D. Bazarov, “Selecting Control Parameters of Mechanical Systems with Servoconstraints”, E3S Web Conf., 264 (2021), 04085
K Khusanov, “Stabilization of mechanical systems with nonholonomic servoconstraints”, IOP Conf. Ser.: Mater. Sci. Eng., 883:1 (2020), 012164
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R G Mukharlyamov, “Modelling of dynamics of mechanical systems with regard for constraint stabilization”, IOP Conf. Ser.: Mater. Sci. Eng., 468 (2018), 012041
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
Haokun Kang, Caishan Liu, Yan-Bin Jia, “Inverse dynamics and energy optimal trajectories for a wheeled mobile robot”, International Journal of Mechanical Sciences, 134 (2017), 576
V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Proc. Steklov Inst. Math., 294 (2016), 222–232
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Historical and critical review of the development of nonholonomic mechanics: the classical period”, Regul. Chaot. Dyn., 21:4 (2016), 455
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