Response of a Discontinuously Non-linear System

Rotor systems with clearances can exhibit chaotic (random-like) motion. Previous work has shown that the embedding space method and correlation dimension estimation can be used to give an indication of the clearance. However some problems were found using this method. The aim of the project is to repeat some of the results as a test case and then to compare the results with a different dynamic system which may show the same type of response. The system will be made up of two masses connected by a massless bar. The bar will be able to contact a spring at some point along its length. The gap (or clearance) between the spring and the bar in the equilibrium point can be modified at one's will. This system replicates some of the features of the rotor system but in a different system. The project tries to find out if a special relation between the clearance of the system and the correlation dimension exists. It will be proved that a relation as a general law can not be found but that in some cases the correlation dimension value can be used to delimit the clearance values.Outgoin

Response of a Discontinuously Non-linear System

Rotor systems with clearances can exhibit chaotic (random-like) motion. Previous work has shown that the embedding space method and correlation dimension estimation can be used to give an indication of the clearance. However some problems were found using this method. The aim of the project is to repeat some of the results as a test case and then to compare the results with a different dynamic system which may show the same type of response. The system will be made up of two masses connected by a massless bar. The bar will be able to contact a spring at some point along its length. The gap (or clearance) between the spring and the bar in the equilibrium point can be modified at one's will. This system replicates some of the features of the rotor system but in a different system. The project tries to find out if a special relation between the clearance of the system and the correlation dimension exists. It will be proved that a relation as a general law can not be found but that in some cases the correlation dimension value can be used to delimit the clearance values.Outgoin

Numerical Integration and Optimization of Motions for Multibody Dynamic Systems

This thesis considers the optimization and simulation of motions involving rigid body systems. It does so in three distinct parts, with the following topics: optimization and analysis of human high-diving motions, efficient numerical integration of rigid body dynamics with contacts, and motion optimization of a two-link robot arm using Finite-Time Lyapunov Analysis.The first part introduces the concept of eigenpostures, which we use to simulate and analyze human high-diving motions. Eigenpostures are used in two different ways: first, to reduce the complexity of the optimal control problem that we solve to obtain such motions, and second, to generate an eigenposture space to which we map existing real world motions to better analyze them. The benefits of using eigenpostures are showcased through different examples.The second part reviews an extensive list of integration algorithms used for the integration of rigid body dynamics. We analyze the accuracy and stability of the different integrators in the three-dimensional space and the rotation space SO(3). Integrators with an accuracy higher than first order perform more efficiently than integrators with first order accuracy, even in the presence of contacts.The third part uses Finite-time Lyapunov Analysis to optimize motions for a two-link robot arm. Finite-Time Lyapunov Analysis diagnoses the presence of time-scale separation in the dynamics of the optimized motion and provides the information and methodology for obtaining an accurate approximation to the optimal solution, avoiding the complications that timescale separation causes for alternative solution methods

Response of a Discontinuously Non-linear System

Rotor systems with clearances can exhibit chaotic (random-like) motion. Previous work has shown that the embedding space method and correlation dimension estimation can be used to give an indication of the clearance. However some problems were found using this method. The aim of the project is to repeat some of the results as a test case and then to compare the results with a different dynamic system which may show the same type of response. The system will be made up of two masses connected by a massless bar. The bar will be able to contact a spring at some point along its length. The gap (or clearance) between the spring and the bar in the equilibrium point can be modified at one's will. This system replicates some of the features of the rotor system but in a different system. The project tries to find out if a special relation between the clearance of the system and the correlation dimension exists. It will be proved that a relation as a general law can not be found but that in some cases the correlation dimension value can be used to delimit the clearance values.Outgoin