Dynamic Systems

Documents about Dynamic Systems

	ME345_Lecture_32 Penn State, ME 345 Excerpt: ... M E 345 Spring 2009 Professor John M. Cimbala Lecture 32 04/03/2009 Today, we will: Finish reviewing the pdf module: Dynamic System Response Do a review example problem 2nd-order dynamic systems Discuss an additional item not in the pdf notes: second-order time constants Do some more example problems 2nd-order dynamic systems Example: Dynamic system response d 2 y dy + + 32 y = x ( t ) . dt 2 dt The forcing function is a step function (sudden jump): x(t) = 0 for t < 0 x(t) = 4 for t > 0 Given: The following second-order ODE: 4 (1) To do: (a) Calculate the equilibrium response. (b) Calculate the damping ratio of this system. Will it oscillate? (c) If the system will oscillate, calculate the oscillation frequency in Hertz [Note: Calculate the physical frequency, not the radian frequency.] Solution: Example: Dynamic system response Given: A pendulum-type amusement park ride behaves as a 2nd-order dynamic system with damping ratio = 0.05 and undamped natural frequenc ...
	exam1-topics Minnesota, MATH 4428 Excerpt: ... 4428: Exam-1 Topics 1. Optimization. Constrained and unconstrained optimization, the method of Lagrange multipliers. Study material and examples: class notes and the theoretical parts of Sect. 1.1-1.3, 2.1-2.3. Some linear optimization problems (Sect ...
	ME345_Lecture_30 Penn State, ME 345 Excerpt: ... M E 345 Spring 2009 Professor John M. Cimbala Lecture 30 03/30/2009 Today, we will: Review the pdf module: Dynamic System Response (1st-order systems) Do some example problems dynamic system response Discuss an additional item not in the pdf n ...
	ME345_Lecture_30 Penn State, ME 345 Excerpt: ... M E 345 Spring 2008 Professor John M. Cimbala Lecture 30 03/31/2008 Today, we will: Review the pdf module: Dynamic System Response Do some example problems dynamic system response Discuss an additional item not in the pdf notes: using the ramp ...
	n6.0 Maryland, GK 161 Excerpt: ... Phys 161: Notes These notes are not complete! Use them in conjunction with the textbook, the lectures, discussion sections, study groups and the website. Lecture 14: F = ma. Recipe for solving simple dynamical systems: 1. Draw a clear diagram of th ...
	ME345_Lecture_31 Penn State, ME 345 Excerpt: ... M E 345 Spring 2008 Professor John M. Cimbala Lecture 31 04/02/2008 Today, we will: Discuss a practical application of 1st-order dynamic system analysis room ventilation Discuss an additional item not in the pdf notes: half-life Finish reviewing the pdf module: Dynamic System Response 2nd-order systems Do some example problems 2nd-order dynamic systems Do Candy Questions for Candy Friday Wednesday (for Exam review) Example a practical example of 1st-order dynamic system analysis Given: A fire has occurred in a hotel room with volume V = 85. m3. Immediately after the fire is extinguished, the mass concentration of hydrogen cyanide (HCN) is ci = 10,000 mg/m3. The firemen blow "fresh" air into the room at V = 28.3 m3/min. Since there is some smoke outside the building, the "fresh" air actually has an ambient mass concentration of HCN equal ca = 1.0 mg/m3. The air is considered safe when the mass concentration of HCN in the room drops below c = 5 mg/m3. To do: Calculate how long the ...
	Math429Description Nevada, MATH 429 Excerpt: ... Math 429/629 Topics in Applied Analysis. Instructors: Chris Herald (herald@unr.edu) and Je Mortensen (jm@unr.edu). Course name: Dynamical Systems Text: (Required) An Introduction to Dynamical Systems, R. Clark Robinson, Pearson Prentice Hall, 2004, I ...
	tutorial2_08 East Los Angeles College, CO 903 Excerpt: ... Complexity Science Doctoral Training Centre CO903 Complexity and Chaos in Dynamical Systems Dynamical systems in R2 1. Solve the initial value problem and sketch the phase portrait x = x + y, y = 4x - 2y, (x0, y0) = (2, -3) 2. Sketch the phase po ...
	Dynamic systems CSU Long Beach, EE 412 Excerpt: ... Introduction to dynamic systems : The dynamic of any situation refers to how the situation changes over the course of time. A dynamical system is a physical setting together with rules for how the setting changes or evolves from one moment of time to the next. One basic goal of the mathematical theory of dynamical systems is to determine or characterize the long-term behavior of the system. Different kinds of dynamical systems have common characteristics: Symbolic, discrete, continuous, and fractal dynamic systems . In the study of dynamic systems we try to determine the future behavior given the past and present behaviors. A classic example studied intensively in the seventies is that of the quadratic functions f(x)=cx(1-x) where c is a fixed real number. The graph of this function is a parabola passing through the x-axis at x=0,1. The maximum value is c/4 occurring at x=.5. An example is shown below: If we restrict c to be nonnegative and less than or equal to 4, the function f(x) has the property that it m ...
	syl Washington, MATH 480 Excerpt: ... Boris Solomyak Padelford C-328, 685-1307 E-mail: solomyak@math.washington.edu Oce hours: M 1-2, T 11-12, or by appointment Web address: http:/www.math.washington.edu/~solomyak/TEACH/480/09/gen.html Math 480 COURSE DESCRIPTION Spring 2009 INTRODUCTIO ...
	contents-08 East Los Angeles College, CO 903 Excerpt: ... Complexity Science Doctoral Training Centre CO903 Complexity and Chaos in Dynamical Systems Lecturer: Dr Yulia Timofeeva (office D2.12, Centre for Complexity Science, Zeeman building) e-mail y.timofeeva@warwick.ac.uk Aims: The module aims to introduc ...
	lecture3 BU, MATH 574 Excerpt: ... Lecture 3: Invariant Measures 1 Finding the attracting set of a dynamical system tells us asymptotically what parts of the phase space are visited, but that is not the only thing of interest about the long-time behavior of a dynamical system. For i ...
	Topic Schedule M435 FA 2006 Colorado State, M 435 Excerpt: ... M435 FA 2006 Due Dates and Topics Schedule Summary of Due Dates 09/01 Draft of simulation project due 09/15 Simulation project due 09/22 Draft of dynamical systems project due 10/06 Dynamical systems project due 10/20 Draft of game theory project due ...
	ME345_Lecture_32 Penn State, ME 345 Excerpt: ... M E 345 Spring 2008 Professor John M. Cimbala Lecture 32 04/04/2008 Today, we will: Finish reviewing the pdf module: Dynamic System Response (2nd-order systems) Do some example problems second-order dynamic systems If time permits, start to review the pdf module: Temperature Measurement Example Given: The following second-order ODE: 5 d 2 y dy + + 1000 y = x ( t ) dt 2 dt The forcing function is a step function (sudden jump): x(t) = 0 for t < 0 x(t) = 25 for t > 0 (a) To do: Calculate the natural frequency and damping ratio of this system. (b) To do: Calculate the equilibrium response (as t , what is y?). Solution: Example Given: A pendulum-type amusement park ride behaves as a 2nd-order dynamic system with damping ratio = 0.05 and undamped natural frequency fn = 0.25 Hz. To do: For an initial displacement Si, calculate the damped natural frequency, the oscillation period, and how long it takes for the oscillations to damp out to within 1% of Si. Solution: Si ...
	lecture_4 UPenn, MATH 170 Excerpt: ... Lecture Notes for Math 170: Ideas in Mathematics (Spring 2007) by Nathanael Leedom Ackerman January 17, 2007 1 1 TALK SLOWLY AND WRITE NEATLY AND BIG! 2 1 TALK SLOWLY AND WRITE NEATLY AND BIG! 2 Misc Collect Homework Mention that the lecture ...
	Schiff_2 Wisconsin, MATH 491 Excerpt: ... Chapter 2 Dynamical Systems . it may happen that small dierences in the initial conditions produce very great ones in the nal phenomena. Henri Poincar e One of the exciting new elds to arise out of 20th century mathematics is that of dynamical syste ...
	MECH370_S07_Ch8_off Contra Costa College, MECH 370 Excerpt: ... MECH370: Modelling, Simulation and Analysis of Physical Systems Chapter 8 Analysis of Dynamical Systems - Transfer Function Analysis Obtaining the complete response using Laplace transform Zero-input response Zero-state response (transfer function, the complex plane and polezero plot, second-order systems, impulse and step responses) Frequency response Properties of transfer function Modelling (Ch. 2,3,4,5,6,9,10,11,12) Simulation (4) Analysis (7,8) Course Outline 1. Definition and classification of dynamic systems (chapter 1) 2. Translational mechanical systems (chapter 2) 3. Standard forms for system models (chapter 3) 4. Block diagrams and computer simulation with Matlab/Simulink (chapter 4) 5. Rotational mechanical systems (chapter 5) 6. Electrical systems (chapter 6) 7. Analysis and solution techniques for linear systems (chapters 7 and 8) 8. Developing a linear model (chapter 9) 9. Electromechanical systems (chapter 10) 10. Thermal and fluid systems (chapters 11, 12) Chapter 6 Lecture Notes on M ...
	outline Minnesota, ME 5281 Excerpt: ... ME 5281 Course Schedule: Fall 2005 Week 1 Sep 6 1) Representation of Dynamic Systems a) ODE representation of systems examples from vehicle control b) Review of Laplace Transforms c) Input-output representation of dynamic systems Sep 8 2) Representation of Dynamic Systems a) State space representation of dynamic systems b) Examples from vehicle control c) Simulation of LTI systems using Matlab Week 2 Sep 13 HW# 1 due 3) The Behavior of Dynamic Systems a) The poles of a transfer function b) Partial fraction expansion of transfer functions c) ODE solutions from transfer functions Sep 15 4) The Behavior of Dynamic Systems a) ODE solutions from transfer functions b) Stability results Week 3 Sep 20 HW# 2 due 5) The Behavior of Dynamic Systems a) State space solution b) Eigenvalues and eigenvectors c) The e At matrix Sep 22 6) The Behavior of Dynamic Systems a) Diagonalization of a matrix b) Stability results Week 4 Sep 27 HW# 3 due 7) Bode Plots a) Magnitude and phase of a complex number b) Review of Bode ...
	outline Minnesota, ME 5281 Excerpt: ... ME 5281/ EE 4231/ AEM 4321 Tentative Course Schedule: Fall 2007 Week 1 Sep 4 1) Representation of Dynamic Systems a) ODE representation of systems examples from vehicle control b) Review of Laplace Transforms c) Input-output representation of dynamic systems Sep 6 2) Representation of Dynamic Systems a) State space representation of dynamic systems b) Examples from vehicle control c) Simulation of LTI systems using Matlab Week 2 Sep 11 HW# 1 due 3) The Behavior of Dynamic Systems a) The poles of a transfer function b) Partial fraction expansion of transfer functions c) ODE solutions from transfer functions Sep 13 4) The Behavior of Dynamic Systems a) ODE solutions from transfer functions b) Stability results Week 3 Sep 18 HW# 2 due 5) The Behavior of Dynamic Systems a) State space solution b) Eigenvalues and eigenvectors c) The e At matrix Sep 20 6) The Behavior of Dynamic Systems a) Diagonalization of a matrix b) Stability results Week 4 Sep 25 HW# 3 due 7) Bode Plots a) Magnitude and phase of a co ...
	lecture5 Allan Hancock College, HOL 105 Excerpt: ... 1. Lecture 4 : Summary A point transformation is a change of generalized coordinates q Q via a diffeomorphism qi = gi(Q, t) , i = 1, . . . , n . (1) Point and Gauge Transformations A Lagrangian gauge transformation is a shift of L, defined by ...
	P002A_Assignment_4 Swarthmore, SOC 002 Excerpt: ... P002A 1st-Year Seminar Assignment #4 Fall 2007 READINGS: RESPONSIBILITY Boccio Boccio notes on fractals - pages 1-20 Stewart - Chapters 11-13, 17 Ruelle - Chapters 11,12 WEBSITE: http:/chaos.swarthmore.edu/courses/SOC002a/i ...
	lecture1 BU, MATH 574 Excerpt: ... Lecture 1; Attractors1 Much of this course will be devoted to understanding the behavior of solutions of dierential equations. If one asks how do solutions of dierential equations behave, the sad answer is, to a rst approximation, in every possible w ...
	PSY260StudyGuide1 Colorado State, PSY 260 Excerpt: ... Child Psych Exam 1 Study Guide T Chapter 1 1. Saying that the study of human development is a science, means that life is a a dynamic system, characterized b change that is multi directional. It is Dynamic, Not Static. It depends on theories, data an ...
	551 University of Illinois, Urbana Champaign, MATH 551 Excerpt: ... Course Schedule - Spring 2008 Mathematics 551 Dynamical Systems Theory credit: 4 hours. Course is an introduction to the study of dynamical systems. Students who intend to do research in nonlinear dynamics are encouraged to take this course. Specific ...
	MA563HomeworkF05 Clarkson, MA 563 Excerpt: ... Homework MA563 Applied Dynamical Systems Fall 2005 Coming VERY soon! ...