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Bolotnik N.,Russian Academy of Sciences | Pivovarov M.,Ilmenau University of Technology 10 05 65 98684 Ilmenau Germany | Zeidis I.,Ilmenau University of Technology 10 05 65 98684 Ilmenau Germany | Zimmermann K.,Ilmenau University of Technology 10 05 65 98684 Ilmenau Germany
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2015

The behavior of a two-body self-propelling locomotion system in a resistive environment is studied. The motion of the system is excited and sustained by means of a periodic change in the distance between the bodies. A complete analysis of the motion of the system is performed for the case where the resistance forces applied by the environment to the bodies of the system are represented by linear functions of the velocities of these bodies relative to the environment. For the case where the resistance forces are nonlinear functions of the velocities of the bodies, a model based on the averaged equation of motion is used. This model assumes the forces of friction acting in the system to be small in comparison with the excitation force. The motion of the system along a horizontal straight line in an isotropic dry friction environment is investigated in detail for two particular types of excitation modes. The calculated results are compared with the experimental data. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.


Bolotnik N.,Russian Academy of Sciences | Pivovarov M.,Ilmenau University of Technology 10 05 65 98684 Ilmenau Germany | Zeidis I.,Ilmenau University of Technology 10 05 65 98684 Ilmenau Germany | Zimmermann K.,Ilmenau University of Technology 10 05 65 98684 Ilmenau Germany
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2015

The motion of self-propelling limbless locomotion systems in a linear viscous environment is considered. The resistance (friction) force acting on an element of the systems is assumed to be proportional to the velocity of this element relative to the environment, the coefficient of proportionality (coefficient of friction) being constant. Two models of interaction of the locomotor with the environment are distinguished. In the first model, the coefficient of friction is constant for a mass element, whereas in the second model, this coefficient is constant for a length element. It is shown that progressive locomotion is impossible for the first model and is possible for the second model. This is explained by the fact that in the second model, the coefficient of friction for a mass element is in fact controlled by changing the length of this element due to deformation of the locomotor's body. The first model applies for lumped mass systems, while the second model is adequate for distributed mass limbless locomotors, like worms. For both models, the equations of motion of the system's center of mass are derived and analyzed. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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