The course covers the basic models and solution techniques for problems of …
The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. We will also discuss approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.
The course addresses dynamic systems, i.e., systems that evolve with time. Typically …
The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions. We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.
This book is a follow-up on Adjustment theory. It extends the theory …
This book is a follow-up on Adjustment theory. It extends the theory to the case of time-varying parameters with an emphasis on their recursive determination. Least-squares estimation will be the leading principle used. A least-squares solution is said to be recursive when the method of computation enables sequential, rather than batch, processing of the measurement data. The recursive equations enable the updating of parameter estimates for new observations without the need to store all past observations. Methods of recursive least-squares estimation are therefore particularly useful for applications in which the time-varying parameters need to be instantly determined. Important examples of such applications can be found in the fields of real-time kinematic positioning, navigation and guidance, or multivariate time series analysis. The goal of this book is therefore to convey the necessary knowledge to be able to process sequentially collected measurements for the purpose of estimating time-varying parameters.
When determining time-varying parameters from sequentially collected measurement data, one can discriminate between three types of estimation problems: filtering, prediction and smoothing. Filtering aims at the determination of current parameter values, while smoothing and prediction aim at the determination of respectively past and future parameter values. The emphasis in this book will be on recursive least-squares filtering. The theory is worked out for the important case of linear(ized) models. The measurement-update and time-update equations of recursive least-squares are discussed in detail. Models with sequentially collected data, but time-invariant parameters are treated first.
In this case only the measurement-update equations apply. State-space models for dynamic systems are discussed so as to include time-varying parameters. This includes their linearization and the construction of the state transition matrix. Elements from the theory of random functions are used to describe the propagation laws for linear dynamic systems. The theory is illustrated by means of many worked out examples. They are drawn from applications such as kinematic positioning, satellite orbit determination and inertial navigation.
This course covers the fundamentals of Newtonian mechanics, including kinematics, motion relative …
This course covers the fundamentals of Newtonian mechanics, including kinematics, motion relative to accelerated reference frames, work and energy, impulse and momentum, 2D and 3D rigid body dynamics. The course pays special attention to applications in aerospace engineering including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. By the end of the semester, students should be able to construct idealized (particle and rigid body) dynamical models and predict model response to applied forces using Newtonian mechanics.
This course reviews momentum and energy principles, and then covers the following …
This course reviews momentum and energy principles, and then covers the following topics: Hamilton’s principle and Lagrange’s equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas.
Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. …
Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange’s equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.
This class is an introduction to the dynamics and vibrations of lumped-parameter …
This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange’s equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems. This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.
Upon successful completion of this course, students will be able to: Create …
Upon successful completion of this course, students will be able to:
Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains Make quantitative estimates of model parameters from experimental measurements Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods Obtain the frequency-domain response of linear systems to sinusoidal inputs Compensate the transient response of dynamic systems using feedback techniques Design, implement and test an active control system to achieve a desired performance measure
Mastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional …
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange’s equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.013J. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject merged with 2.003.
These dynamics course notes were authored by Dr. Elizabeth Croft (currently at …
These dynamics course notes were authored by Dr. Elizabeth Croft (currently at Monash University (elizabeth.croft@monash.edu) in 2004, and converted for open licensing (including figure creation) in 2019 by Dr. Agnes d'Entremont (adentremont@mech.ubc.ca) from the Department of Mechanical Engineering at the University of British Columbia, Vancouver, Canada (https://mech.ubc.ca).
The notes (are designed to be used for a second-year dynamics course in Mechanical Engineering, and cover planar rigid-body dynamics and an introduction to one degree-of-freedom vibrations. The order of topics has vibrations earlier in the series than typical, due to their use in an integrated course. This order matches the course timing of related ordinary differential equation solutions in the integrated mathematics and electric circuits courses.
These notes are intended to be skeleton notes, with substantial portions (diagrams, derivations, solutions) written in by students along with their instructor. Completed notes are included. PDF notes plus original LaTeX code and editable images (Powerpoint) are available at the link.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
In this class we will critically review both classical works and recent …
In this class we will critically review both classical works and recent literature on complexity in ecology. The emphasis will be on developing quantitative theories in the context of experimental and observational data. We will meet twice weekly for roundtable discussions.
In this class we will critically review both classical works and recent …
In this class we will critically review both classical works and recent literature on ecological theory. Emphasis will be on providing a theoretical and phenomenological foundation for the study of computational models. We will meet twice weekly for roundtable discussions.
This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: …
This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov’s first and second methods; feedback linearization; and application to nonlinear circuits and control systems.
This course begins with a study of the role of dynamics in …
This course begins with a study of the role of dynamics in the general physics of the atmosphere, the consideration of the differences between modeling and approximation, and the observed large-scale phenomenology of the atmosphere. Only then are the basic equations derived in rigorous manner. The equations are then applied to important problems and methodologies in meteorology and climate, with discussions of the history of the topics where appropriate. Problems include the Hadley circulation and its role in the general circulation, atmospheric waves including gravity and Rossby waves and their interaction with the mean flow, with specific applications to the stratospheric quasi-biennial oscillation, tides, the super-rotation of Venus’ atmosphere, the generation of atmospheric turbulence, and stationary waves among other problems. The quasi-geostrophic approximation is derived, and the resulting equations are used to examine the hydrodynamic stability of the circulation with applications ranging from convective adjustment to climate.
In the past few years, we have seen a rapid expansion in …
In the past few years, we have seen a rapid expansion in the field of mobile computing due to the pro- liferation of inexpensive, widely available wireless devices or networks.However, all these networks are conventional wireless networks as they require a fixed network infrastructure with cen- tralised administration for their operation, potentially consuming a lot of time and money for set-up and maintenance.Drawbacks of conventional wireless networks are driving a new alternative way for mobile communication, in which mobile devices form a selfcreating, self-organising and self-administering wireless network, called a mobile ad hoc network.In mobile ad-hoc networking (MANETs), nodes communicate to each other based on public identities. In this paper,for a position based routing[22] an innovative packet forwarding mechanism is proposed in which source node generates route request packet and broadcast packet to other neighbor nodes to locate destination by implementing black hole attack[8]. Proposed E-APSAR (Enhanced Anonymous Position Based security aware routing protocol) is implemented on NS-2 and results shown significant improvement over original DSR in terms of various performance metrics. It has been found that on dense network certain numbers of malicious nodes are supportive to reducing communication overhead and because of density negative effect of malicious attacks which is proposed E-APSAR that is able to reduce. Hence result shows proposed E-APSAR will be helpful to decrease communication overhead.
Students further their understanding of the engineering design process (EDP) while applying …
Students further their understanding of the engineering design process (EDP) while applying researched information on transportation technology, materials science and bioengineering. Students are given a fictional client statement (engineering challenge) and directed to follow the steps of the EDP to design prototype patient safety systems for small-size model ambulances. While following the steps of the EDP, students identify suitable materials and demonstrate two methods of representing solutions to the design challenge (scale drawings and small-scale prototypes). A successful patient safety system meets all of the project's functions and constraints, including the model patient (a raw egg) "surviving" a front-end collision test with a 1:8 ramp pitch.
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