Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Investigation of synchroniser engagement in dual clutch transmission equipped powertrains

Transient response of a dual clutch transmission (DCT) powertrain to synchroniser mechanism engagements is investigated using a lumped inertia model of the powertrain. Original research integrates lumped inertia powertrain models for the DCT with a detailed synchroniser mechanism model and two separate engine models, comprising of a mean torque model and a harmonic torque model, using torque derived from piston firing. Simulations are used to investigate the synchroniser mechanism engagement process in a previously unscrutinised operating environment. Simulations are performed using both engine torque models, with the mean torque model demonstrates the highly nonlinear nature of synchroniser mechanism engagement, and the powertrain response to the engagement process. Through the introduction of harmonic engine torques, additional excitation is present in the mechanism during engagement, and increased vibration of the synchroniser sleeve results. The impact of vibrations is particularly important to the increased wear of indexing chamfer contact surfaces. © 2011 Elsevier Ltd All rights reserved

A fully configurable virtual laboratory of classical mechanics

Dissertação de mestrado em Computer ScienceNowadays many mathematical applications allow the user to introduce its own equations in the system and also observe through different possibilities the desired results. Regarding physics, an extended range of virtual laboratories allow the user to accomplish virtual physics experiments. These virtual laboratories consist in predefined scenarios where the user can change the value of the physics variables and then visualise the changes accomplished. Other virtual laboratories uses a physics engine allowing the user to create its own scenarios. However, the physical behaviour of the objects is hardcoded since it results strictly on the physics equations used internally by the physics engine. This dissertation pretends to investigate how far and with what degree of scientific rigor it is possible to associate the idea of the user introducing its own equations with the idea of accomplishing virtual experiments of physics. As a proof of concept, this dissertation focus on a specific area of mechanics: the dynamic of rigid bodies. The result of this research is a virtual laboratory completely different relatively the others. Our system has no knowledge about physics. Even the most general laws of physics such as the Newton’s second law are not known by the system. To the system, any equation introduced is considered just as one more equation without any particular meaning associated to it. The same happens for any physics entity. For example, if the gravitational acceleration is introduced by the user, to the system it is just another attribute of the world. Taking into account the dynamics of rigid bodies, an object can be identified as being, at any time, in one of three different states. These are: when a object is not in contact with any other, when an object collides with another object and they immediately separate, and when two objects remain in contact over time. The user must specify all the equations that drive each of these three states. Using its geometrical knowledge, the engine determines at any time in which state an object is. Also, the system provides all the relevant geometrical information. For instance, in a collision between two objects, the point and the two normals vectors of the collision are provided. The graphical simulations reflects strictly on the equations introduced. Therefore, if the equations to solve a collision between two objects does not reflect the real underlying physics of the situation, it is possible that the objects simply ends-up penetrating each other. All the relevant numerical information about an experience can be processed through different forms. In fact, the user can request plots of variables, the graphical application of vectors on objects, and even the tracing of the variables at a specific event

Modia3D: Modeling and Simulation of 3D-Systems in Julia

Modia3D is an experimental Julia package to model and simulate 3D mechanical systems. Ideas from modern game engines are used to achieve a highly flexible setup and features of multi-body algorithms are used to get a rigid mathematical formulation and support, for example, of closed kinematic loops. Collision handling is performed on convex geometries with elastic response calculation. A Modia3D model is solved with a variable-step solver. This is important to combine Modia3D with the equation-based modeling system Modia in the future

Underactuated Attitude Control of a CubeSat Using Cold Gas Thrusters and Nonlinear Control Methods

Impulsive thrusters on small satellites, such as CubeSats, are typically used for attitude control. However, to become more agile, small CubeSats must also look to propulsion systems utilizing impulsive thrusters, such as cold-gas, for translational maneuvers. The combined thrust vector is often misaligned with the system\u27s center of mass resulting in a disturbance torque. This must be counteracted by either an attitude determination and control system (ADCS), additional thrusters, or a control method to keep the satellite\u27s attitude at or near equilibrium. Nonlinearities generated by the impulsive maneuvers are overcome via control techniques explored in this research to include on-off control, sliding mode control, and model reference adaptive control (MRAC). These methods were then compared to a baseline test without thruster modulation, where the reaction wheels must de-saturate prior to continuing the maneuver. For a 1.5 m/s delta-v maneuver, the nonlinear control techniques completed the maneuver nearly 100 times faster than the baseline, while improving pointing accuracy throughout the burn by up to 5%

The Efficiency of Magnetic Field Amplification at Shocks by Turbulence

Turbulent dynamo field amplification has often been invoked to explain the strong field strengths in thin rims in supernova shocks ($\sim 100 \, \mu$G) and in radio relics in galaxy clusters ($\sim \mu$G). We present high resolution MHD simulations of the interaction between pre-shock turbulence, clumping and shocks, to quantify the conditions under which turbulent dynamo amplification can be significant. We demonstrate numerically converged field amplification which scales with Alfv\'en Mach number, $B/B_0 \propto {\mathcal M}_{\rm A}$, up to ${\mathcal M}_{\rm A} \sim 150$. This implies that the post-shock field strength is relatively independent of the seed field. Amplification is dominated by compression at low ${\mathcal M}_{\rm A}$, and stretching (turbulent amplification) at high ${\mathcal M}_{\rm A}$. For high $\mathcal{M}_{\rm A}$, the $B$-field grows exponentially and saturates at equipartition with turbulence, while the vorticity jumps sharply at the shock and subsequently decays; the resulting field is orientated predominately along the shock normal (an effect only apparent in 3D and not 2D). This agrees with the radial field bias seen in supernova remnants. By contrast, for low $\mathcal{M}_{\rm A}$, field amplification is mostly compressional, relatively modest, and results in a predominantly perpendicular field. The latter is consistent with the polarization seen in radio relics. Our results are relatively robust to the assumed level of gas clumping. Our results imply that the turbulent dynamo may be important for supernovae, but is only consistent with the field strength, and not geometry, for cluster radio relics. For the latter, this implies strong pre-existing $B$-fields in the ambient cluster outskirts.Comment: 15 pages, 11 figures, published version on MNRA