Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
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Ivan Polekhin
Abstract
The problem of motion of a rigid body with a fixed point is considered. We study qualitatively the solutions of the system after Routh reduction. For the Lagrange integrable case, we show that the trajectories of solutions starting at the boundary of a possible motion area can both cover and not cover the entire possible motion area. It distinguishes these systems from the systems without gyroscopic forces, where the trajectories always cover the possible motion area. We also present some numerical and analytical results on the same matter for the Kovalevskaya case.
Acknowledgements
I would like to thank the reviewer for the valuable suggestions concerning the structure and the content of the manuscript.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
- Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
- Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
- Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
- Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
- A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
- New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
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- Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
- Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
- Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
- Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
- Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
- Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
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Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
- Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
- Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
- Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
- Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
- A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
- New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
- Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach
- Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
- A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems
- The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach
- Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
- The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
- Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
- Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
- Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
- Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
- Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
- Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
- Results on Controllability of Nonlinear Hilfer Fractional Stochastic System
- Effects of Different Turbulence Models on Three-Dimensional Unsteady Cavitating Flows in the Centrifugal Pump and Performance Prediction
