The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggested model is capable of describing oblique impacts of spherical bodies, which can be important in many applications, including dynamical simulation of granular materials. We find that the behaviour of the bouncing fly-wheel is sensitive to the initial conditions, and the escape time plots are used to illustrate this observation.
Due to their small sizes molecular systems are often overdamped. Conformational changes in these molecules are a consequence of the separation of the energy input between the different displacements and velocities of the different functional sites of the molecule. We show how a simple mechanical device, that splits the forces between the different parts of the system, can achieve spatial (displacements) and temporal (velocities) separation. As a result of the overdamped nature of the motion, the equations can be decoupled by introducing a damping center. As a particular example, we briefly discuss myosin II, a motor protein responsible for the contraction of skeletal muscles.
KeywordsOverdamped dynamics · multiple spatial scales · multiple time scales · myosin II Acknowledgement Financial support from OTKA under grant no. K 68415 and IN 82349 are hereby gratefully acknowledged. We are indebted for the valuable discussions with Mihály Kovács.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.