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Articles 1 - 6 of 6
Full-Text Articles in Non-linear Dynamics
Rocket Powered Flight As A Perturbation To The Two-Body Problem., Clayton Jeremiah Clark
Rocket Powered Flight As A Perturbation To The Two-Body Problem., Clayton Jeremiah Clark
Electronic Theses and Dissertations
The two body problem and the rocket equation r̈ + ∊ α ṙ + k/r3r = 0 have been expressed in numerous ways. However, the combination of the rocket equation with the two-body problem has not been studied to any degree of depth due to the intractability of the resulting non-linear, non-homogeneous equations. The goal is to use perturbation techniques to approximate solutions to the combined two-body and rocket equations.
Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov
Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov
Articles
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.
An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
Articles
Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system and are universal for a given system. The anharmonic oscillator is chosen as an example and is discussed for different choices of its physical parameters. It is shown that the typical approach for the determination of the Volterra Series representation is not valid for the important case when the nonlinear system exhibits oscillatory behaviour and the input has a pole …
Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman
Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eceentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature …
A Solvable Model For Gravity Driven Granular Dynamics, J. J. P. Veerman
A Solvable Model For Gravity Driven Granular Dynamics, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We discuss a toy model to study the dynamics of individual particles in avalanches. The model describes a particle launched from an inclined infinite staircase. The particle is not allowed to bounce when it collides with the staircase. During the collision, the particle loses some energy, and after that slides on to the end of the step it landed on. The process then repeats itself. The dynamics of this no-bounce model can essentially be completely understood. Partial versions of some results were stated and argued in previous work. Here we give a full description together with all the proofs. We …
On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov
On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov
Articles
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.