Многочленный маятник
Многие знают, что уже двойной плоский маятник (из задачки на составление функции Лагранжа из "Механики" Ландавшица, Оля dsgtq_qfle, помнишь?:) демонстрирует хаотическую динамику (на этот счет можно найти красивые демюнстрации на ЮТьюбе). Ниже мощный учебно-конструкторско-методический текст на этот счет на 72 страницы:
The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control: https://arxiv.org/abs/2205.06231
Kadierdan Kaheman, Urban Fasel, Jason J. Bramburger, Benjamin Strom, J. Nathan Kutz, Steven L. Brunton
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors, from simple harmonic motion in the single pendulum to chaotic dynamics in multi-arm pendulums. Under forcing, even the single pendulum may exhibit chaos, providing a simple example of a damped-driven system. All multi-armed pendulums are characterized by the existence of index-one saddle points, which mediate the transport of trajectories in the system, providing a simple mechanical analog of various complex transport phenomena, from biolocomotion to transport within the solar system. Further, pendulum systems have long been used to design and test both linear and nonlinear control strategies, with the addition of more arms making the problem more challenging. In this work, we provide extensive designs for the construction and operation of a high-performance, multi-link pendulum on a cart system. Although many experimental setups have been built to study the behavior of pendulum systems, such an extensive documentation on the design, construction, and operation is missing from the literature. The resulting experimental system is highly flexible, enabling a wide range of benchmark problems in dynamical systems modeling, system identification and learning, and control. To promote reproducible research, we have made our entire system open-source, including 3D CAD drawings, basic tutorial code, and data. Moreover, we discuss the possibility of extending our system capability to be operated remotely to enable researchers all around the world to use it, thus increasing access.
Comments: 72 pages, 39 figures, 9 tables
The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control: https://arxiv.org/abs/2205.06231
Kadierdan Kaheman, Urban Fasel, Jason J. Bramburger, Benjamin Strom, J. Nathan Kutz, Steven L. Brunton
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors, from simple harmonic motion in the single pendulum to chaotic dynamics in multi-arm pendulums. Under forcing, even the single pendulum may exhibit chaos, providing a simple example of a damped-driven system. All multi-armed pendulums are characterized by the existence of index-one saddle points, which mediate the transport of trajectories in the system, providing a simple mechanical analog of various complex transport phenomena, from biolocomotion to transport within the solar system. Further, pendulum systems have long been used to design and test both linear and nonlinear control strategies, with the addition of more arms making the problem more challenging. In this work, we provide extensive designs for the construction and operation of a high-performance, multi-link pendulum on a cart system. Although many experimental setups have been built to study the behavior of pendulum systems, such an extensive documentation on the design, construction, and operation is missing from the literature. The resulting experimental system is highly flexible, enabling a wide range of benchmark problems in dynamical systems modeling, system identification and learning, and control. To promote reproducible research, we have made our entire system open-source, including 3D CAD drawings, basic tutorial code, and data. Moreover, we discuss the possibility of extending our system capability to be operated remotely to enable researchers all around the world to use it, thus increasing access.
Comments: 72 pages, 39 figures, 9 tables