gearsInMesh
Create gearsInMesh object. The object is handle class object.
Syntax
gearsInMesh(g1,g2)
Description
gearsInMesh(g1,g2) create gearInMesh object with gears g1 and g2 in mesh
Input arguments
g1, g2 - gear object. Module of the gears must be equal
Properties
G1, G2 - gear objects
a - center distance
alphaw - working (operating) pressure angle
Object functions
plot
draw gears in mesh
Syntax
plot(GM) draw gears GM.G1 and GM.G2 in mesh
plot(__,'-th1',th1) specify initial rotation angle th1 of the first gear GM.G1.
plot(__,'-zoom',fac) specify zoom factor fac in units of module.
plot(__,'-a',a) specify center distance a
plot(__,'-np',np) specify number of points for gears contour
Input arguments
GM - gearsInMesh object
Optional input arguments
'save' - save figure to jpg file
Optional name-value input arguments
'-a',a - center distance. Default value is a = GM.a
'-np',np - number of points used to approximate gear profile. Defult value is 20.
'-th1',th1 - initial rotation angle in degrees of gear g1. Default value is 0.
'-zoom',fac - zoom factor in units of module. E.g. if fac=3 the display window is (-3m+g1.R,3m+g1.R,-3m,3m) where m is module and g1.R radius of gear 1 pitch circle. Default value is no zoom
animate
draw succesive positions of gears in mesh
Syntax
animate(GM) animate gears GM.G1 and GM.G2 in mesh
animate(__,'-dth1',dth1) specify step of rotation angle dth1 of the first gear GM.G1.
animate(__,'-zoom',fac) specify zoom factor fac in units of module.
animate(__,'-a',a) specify center distance a
animate(__,'-np',np) specify number of points for gears contour
animate(__,'-nr',nr) specify number of turns of gear 1
Input arguments
GM - gearsInMesh object
Optional input arguments
'save' - create avi movie
Optional name-value input arguments
'-a',a - center distance. Default value is GM.a
'-nr',nr - number of rotation of gear 1. Default value is 1.
'-np',np - number of points used to approximate gear profile. Defult value is 20.
'-dth1',dth1 - step of rotation angle in degrees of gear MG.G1. Default value is 0.5 degrees.
'-zoom',fac - zoom factor in units of module. E.g. if fac=3 the display window is (-3m+MG.G1.R,3m+MG.G1.R,-3m,3m) where m is module and MG.G1.R radius of gear 1 pitch circle. Default value is no zoom
Examples
% the examples will work only with draw19 library
addpath('..\draw2d')
Example1
% define gear rack with module 1mm
a = gearRack(1);
% define 9-tooth and 9-tooth gears
G1 = gear(a,5);
Dynamical Systems with Applications using MATLAB
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DYNAMICAL SYSTEMS WITH APPLICATIONS USING MATLAB %
% COPYRIGHT BIRKHAUSER 2004 STEPHEN LYNCH %
% PUBLISHED June 2004 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
CONTENTS
Preface
0. A Tutorial Introduction to MATLAB and the Symbolic Math Toolbox
0.1 Tutorial One: The Basics and the Symbolic Math Toolbox (1 Hour)
0.2 Tutorial Two: Plots and Differential Equations (1 Hour)
0.3 MATLAB Program Files, or M-Files
0.4 Hints for Programming
0.5 MATLAB Exercises
1. Linear Discrete Dynamical Systems
1.1 Recurrence Relations
1.2 The Leslie Model
1.3 Harvesting and Culling Policies
1.4 MATLAB Commands
1.5 Exercises
2. Nonlinear Discrete Dynamical Systems
2.1 The Tent Map and Graphical Iterations
2.2 Fixed Points and Periodic Orbits
2.3 The Logistic Map, Bifurcation Diagram, and Feigenbaum Number
2.4 Gaussian and Henon Maps
2.5 Applications
2.6 MATLAB Commands
2.7 Exercises
3. Complex Iterative Maps
3.1 Julia Sets and the Mandelbrot Set
3.2 Boundaries of Periodic Orbits
3.3 MATLAB Commands
3.4 Exercises
4. Electromagnetic Waves and Optical Resonators
4.1 Maxwell's Equations and Electromagnetic Waves
4.2 Historical Background of Optical Resonators
4.3 The Nonlinear Simple Fibre Ring Resonator
4.4 Chaotic Attractors and Bistability
4.5 Linear Stability Analysis
4.6 Instabilities and Bistability
4.7 MATLAB Commands
4.8 Exercises
5. Fractals and Multifractals
5.1 Construction of Simple Examples
5.2 Calculating Fractal Dimensions
5.3 A Multifractal Formalism
5.4 Multifractals in the Real World and Some Simple Examples
5.5 MATLAB Commands
5.6 Exercises
6. Controlling Chaos
6.1 Historical Background
6.2 Controlling Chaos in the Logistic Map
6.3 Controlling Chaos in the Henon Map
6.4 MATLAB Commands
6.5 Exercises
7. Differential Equations
7.1 Simple Differential Equations and Applications
7.2 Applications to Chemical Kinetics
7.3 Applications to Electric Circuits
7.4 Existence and Uniqueness Theorem
7.5 MATLAB Commands
7.6 Exercises
8. Planar Systems
8.1 Canonical Forms
8.2 Eigenvectors Defining Stable and Unstable Manifolds
8.3 Phase Portraits of Linear Systems in the Plane
8.4 Linearization and Hartman's Theorem
8.5 Constructing Phase Plane Diagrams
8.6 MATLAB Commands
8.7 Exercises
9. Interacting Species
9.1 Competing Species
9.2 Predator-Prey Models
9.3 Other Characteristics Affecting Interacting Species
9.4 MATLAB Commands
9.5 Exercises
10. Limit Cycles
10.1 Historical Background
10.2 Existence and Uniqueness of Limit Cycles in the Plane
10.3 Non-Existence of Limit Cycles in the Plane
10.4 Exercises
11. Hamiltonian Systems, Lyapunov Functions, and Stability
11.1 Hamiltonian Systems in the Plane
11.2 Lyapunov Functions and Stability
11.3 MATLAB Commands
11.4 Exercises
12. Bifurcation Theory
12.1 Bifurcations of Nonlinear Systems in the Plane
12.2 Multistability and Bistability
12.3 MATLAB Commands
12.4 Exercises
13. Three-Dimensional Autonomous Systems and Chaos
13.1 Linear Systems and Canonical Forms
13.2 Nonlinear Systems and Stability
13.3 The Rossler System and Chaos
13.4 The Lorenz Equations, Chua's Circuit, and the Belousov-Zhabotinski Reaction
13.5 MATLAB Commands
13.6 Exercises
14. Poincare Maps and Nonautonomous Systems in the Plane
14.1 Poincare Maps
14.2 Hamiltonian Systems with Two Degrees of Freedom
14.3 Nonautonomous Systems in the Plane
14.4 MATLAB Commands
14.5 Exercises
15. Local and Global Bifurcations
15.1 Small-Amplitude Limit Cycle Bifurcations
15.2 Melnikov Integrals and Bifurcating Limit Cycles from a Center
15.3 Homoclinic Bifurcations
15.4 MATLAB Commands
15.5 Exercises
16. The Second Part of David Hilbert's 16'th Problem
16.1 Stateme
