updated June 28, 2014

These are some Mathematica CDF apps that I wrote over the last few years. These can be run using the free Mathematica CDF player available from Wolfram CDF plugin webpage

These are updated all the time as needed. The current version of each app is given by the date of the modification posted below the name of the application.

Clicking the image will run a small animation made using an animated gif file. Clicking the run link below the image opens a new web page where the CDF will automatically load and run inside the web page. Many of those pages contain more documentation on the application. Some have separate reports.

The CDF and the notebook are also available using the links below the image to download and run locally.

Solve wave equation u_tt = c^2 u_xx using leapfrog method
### 57 solve wave equation $u_{tt}= c^2 u_{xx}$ using leap frog method

### 56 Symmetric top gyro motion

### 55 Effect on precession due to spinning wheel

### 54 Spinning wheel

### 53 Rotation stability of 3D cube

### 52 Rotation stability of cylinder

### 51 simple spring/mass/damper simulation

### 50 simple spring/mass/damper simulation with stop bar

### 49. three pendulums with two springs

### 48. Simulation of rigid body dynamics

### 47. Another rigid body dynamics

### 46. Direct and Shear Strain Deformation in 3D

### 45. Finite Difference Formulas

### 44. 2D rectangular membrane modal analysis

### 43. Generalized Single Degree Of Freedom Method

### 42 Vibration analysis of forced single degree freedom system

### 41 Vibration analysis of free unforced single degree freedom system

### 40 Showing velocity and acceleration components for circular motion

### 39 Adding Gaussian noise to signal using SNR

### 38 elliptical satellite motion demo

### 37. Double pendulum using heavy spring

### 36. particles collision simulation

### 35. Spring Mass System On a Rotating Table

### 34. Triple pendulum with damping

### 33. Chaotic motion of damped driven pendulum

### 32. Mass on a spring at end of a solid pendulum

### 31. Rigid body disk pendulum rotating on moving table

### 30. Rigid body pendulum on a flywheel

### 29. Direct dynamics for simulation of pendulum

### 28. cylinders with 3 springs

### 27. LQR Control of inverted pendulum on moving cart

### 26. PID controller design for second order system

### 24. Single span Euler Bernoulli beam

### 23. finite element Ritz method for axially loaded beam

### 22. Solving 2D Poisson PDE on non-uniform rectangle grid

### 21. solving Helmholtz differential equation in 2D using finite difference

### 20. solving Helmholtz differential equation in 1D using finite difference

### 19. Solving diffusion-advection-reaction (heat) in 1D

### 18. Finite difference solution of the diffusion-convection in 1D

### 17. Minimal example to solve Poisson 2D using Jacobi method

### 16. Finite difference for solving Poisson PDE on unit square

### 15. Phase plane plot of the Van der Pol differential equation

### 14. Design a digital filter by geometric means

### 13. Fourier series coefficients of a rectangular pulse signal

### 12. From continuous-to-discrete time Fourier transform by sampling

### 11. Analog-to-discrete system conversion using impulse invariance

### 9. Power efficiency of amplitude modulation

### 8. Rectangular pulse and its Fourier transform

### 7. sinc interpolation to reconstruct a signal from its sample

### 6. Power content of frequency modulation and phase modulation

### 5. IIR digital low-pass Filter Design by Butterworth method

### 4. Computed tomography using Radon Transform (incremental angles)

### 3. Computed tomography using Radon Transform

Version: July 5, 2014

boundary conditions are fixed on left and right side. Initial speed is zero. Select initial data and see the wave move..nb | .cdf | listing | run |

Version: June 30, 2014

Adjust the initial wheel spin for symmetric gyro top and watch the effect on motion..nb | .cdf | listing | run |

Version: June 29, 2014

Modify the wheel spin rate, its radius and distance from the support and see the effect on the precession spin rate..nb | .cdf | listing | run |

Version: June 29, 2014

Adjust the radius, number of rods and angle to see the wheel spin in 3D.nb | .cdf | listing | run |

Version: June 28, 2014

Cube is stable when spinning around either the major or the minor principal axes. This demo illustrates this by solving Euler equations of motion in 3D for zero torque. Select the spin axes, then click on perturbe to see the effect..nb | .cdf | listing | run |

Version: June 28, 2014

Cylinder is a solid object which has one unique moment of inertia, which is around the z-axis. When it is spinning around z-axis, and perturbed it will remain stable. If it was spinning around either the x or the y axes then perturbed, it will become unstable. This demo illustrates this by solving Euler equations of motion in 3D for zero torque..nb | .cdf | listing | run |

Version: June 19, 2014

Change the mass, stiffness or damping and see the effect on motion of mass. No stop bar..nb | .cdf | listing | run |

Version: June 19, 2014

Change the mass, stiffness or damping and see the effect on motion of mass. When mass hits the bar, it bounces back..nb | .cdf | listing | run |

Version: August 16, 2013

This Demonstration simulates the equations of motion of three rigid pendulums A, B, C with a spring attached from the end of A to the end of B and another spring attached from the end of B to the end of C.

.nb | .cdf | listing | run |

Version: Dec 19, 2013

Final project EMA 542. Two noncollinear rotating bodies.

.nb | .cdf | listing | report | run |

Version: Dec 19, 2013

Solving EMA 542 HW3 problem 1

.nb | .cdf | listing | run |

Version: sept 7, 2013

Shows effect of change in $E$ and Poisson ratio on normal stresses and shear stresses. Shows the 3D deformation in an isotropic unit volume (pure shear).

.nb | .cdf | listing | run |

Version: August 29, 2013

Generated By Interpolating Polynomial. Shows error in approximation based on which formula used.

.nb | .cdf | listing | run |

Version: July 31 2013

PDE solved is $\frac{\partial^2 w}{\partial^2 x}+\frac{\partial^2 w}{\partial^2 y}=\frac{1}{c} \frac{\partial^2 w}{\partial^2 t}$ Where $w(x,y,t)$ is the amplitude of the wave.

.nb | .cdf | listing |

report | run |

Version: July 28 2013

Generalized Single Degree Of Freedom Method For Wind Tower Structure. Estimating natural frequency for industrial wind tower using the method of generalized single degree of freedom

.nb | .cdf | listing | run |

Version: August 29 2013

Solving $m u''+c u'+k u=F \sin(\varpi t)$ vibration, resonance, critical damping, beat beat phenomenon, impulse response, magnification factor

.nb | .cdf | listing | run |

Version: July 24 2013

.nb | .cdf | listing | run |

Version: January 4 2014

Simple demo that shows a particle moving in circular orbit. Vectors show the current velocity and the red colored vectors show the centrifugal and tangential accelerations. The length of the vectors is made to be proportional to the magnitudes..nb | .cdf | listing | run |

Version: June 21 2014

Specify the SNR and see the Gaussian noise added. The larger the SNR, the less the noise. SNR represents the ratio of the variance of the signal to the noise. For a signal, and cosine is used from zero to 2 PI..nb | .cdf | listing | run |

Version: Jan 24, 2014

Change the ellipse eccentricity and see the effect on motion of satellite..nb | .cdf | listing | run |

Version: Sept 10, 2012

Three degrees of freedom, Lagrangian method, Rayleigh factor, effective weight of spring.nb | .cdf | listing | |

report: | HTML | .nb | |

run |

Version: Sept 25, 2012

collision detection using priori (continuous) detection. Supports up to 8 particles..nb | .cdf | listing |

report | run |

Version: August 8, 2012

moment of inertia, rotation dynamics, spring-mass on spinning disk.nb | .cdf | listing |

report | run |

Version: September 1, 2011

Triple, double and simple pendulum, damped medium. Lagrangian. phase portrait.nb | .cdf | listing |

run |

Version: September 2, 2011

Bifurcation, Poincare map, Power Spectrum, Phase Portrait.nb | .cdf | listing | run |

Version: Nov 10, 2012

Lagrangian method, spring mass, NDSolve.nb | .cdf | listing | |

report: | HTML | .nb | |

run |

Version: June 25, 2011

Lagrangian, principal moments of inertia, angular momentum $\frac{dL}{dt}$, 3 nonlinear equations of motion, numerical solution with NDSolve using direct Dynamics without using Manipulate.nb | .cdf | listing | run |

Version: June 8, 2011

2 degrees of freedom: $\theta$, the pendulum's swing angle, and $\phi$ the flywheel's rotation angle. two nonlinear equations, Lagrangian energy method.nb | .cdf | listing | run |

Version: Nov 10, 2012

simulation of damped and driven pendulum with chaotic motion using direct Dynamics without using Manipulate.nb | .cdf | listing | run |

Version: July 26,2013

Simulation of motion of 2 masses connected by 3 springs. Equations derived using the Lagrangian energy method.nb | .cdf | listing |

report | run |

Version: April 16, 2012

.nb | .cdf | listing | run |

Version: Feb 2, 2012

P, PI, PD, or PID. simulate the plant with and without the controller, Bode, Nyquist, open and closed loop.nb | .cdf | listing | run |

Version: Oct 21 2009

deflection curve of beam, bending moment, shear diagrams, point load, distributed load, external moment, deflection ratio.nb | .cdf | listing | run |

Version: 6/2/2012

deflection curve of beam, bending moment, shear diagrams, point load, distributed load, external moment, deflection ratio.nb | .cdf | listing |

report | run |

Version: May 30, 2014

$-\nabla^2 u=f(x,y)$, Neummann, Dirichlet B.C. direct, Jacobi, Gauss-Seidel, Gauss-Seidel red/black, SOR, Chebyshev, steepest descent, conjugate gradient, GMRES, BiCGSTAB, sparse matrices.nb | .cdf | listing | run |

Version: Feb 2, 2012

solving $-\nabla^2 u-k^2 u=f(x,y)$ in 2D, Dirichlet, Sommerfeld B.C..nb | .cdf | listing | run |

Version: March 6, 2012

solving $-U_{xx} -k^2 U=f(x)$ in 1D, Dirichlet, Sommerfeld B.C..nb | .cdf | listing | run |

Version: Feb 20, 2012

solving $c\,u_{xx}=d\,u_t+a\,u+f(x,t)$ in 1D. Neummann, Dirichlet B.C..nb | .cdf | listing | run |

Version: Feb 10, 2012

solving $c\, u_{xx}=d\, u_t+a\, u_x$ in 1D, Dirichlet, Neummann B.C..nb | .cdf | listing | run |

Version: March 6, 2012

.nb | .cdf | listing | run |

Version: Nov 14, 2010

small example, numerical solution of $\Delta^2u=-e^{-(x-0.25)^2-(y-0.6)^2}$ on unit square, Dirichlet B.C..nb | .cdf | listing | run |

Version: April 12 2009

phase plot ($x'(t)$ vs. $x(t)$), Van der Pol nonlinear differential equation for different initial conditions.nb | .cdf | listing |

report | run |

Version: April 12 2009

select poles and zero locations with mouse, magnitude spectrum, BodePlot, Stability Margins, Nyquist, Nichols, root locus, S-plane map,region of convergence, convert H(z) to H(s).nb | .cdf | listing | run |

Version: April 12 2009

plot magnitude and phase of the Fourier coefficients for a rectangular pulse train signal, sinc function.nb | .cdf | listing | run |

Version: April 7 2010

Relation between continuous time Fourier transform (CTFT) of a continuous time signal $x_a(t)$ and discrete time Fourier transform (DTFT) of the discrete signal $x(n)$, sampling.nb | .cdf | listing | run |

Version: May 3, 2010

Applied to second order system, sampling, poles, zeros, $H(z)= \sum\limits_{i=1}^N \frac{T\, A_i}{1-z^{-1} \exp(p_i\, T)}$, $H(s)= \sum\limits_{i=1}^N \frac{A_i}{s-p_i}$.nb | .cdf | listing | run |

Version: August 31 2009

Illustrates the effect of changing the modulation factor on the power efficiency of ordinary amplitude modulation (AM).nb | .cdf | listing | run |

Version: December 27 2009

Manipulate a rectangular pulse signal and observe how its Fourier transform changes.nb | .cdf | listing | run |

Version: Feb 18 2010

Manipulate a rectangular pulse signal and observe how its Fourier transform changes.nb | .cdf | listing | run |

Version: September 6 2009

BesselJ, modulation index, carrier frequency, carrier amplitude, deviation constant, bandwidth of the modulated carrier, power ratio..nb | .cdf | listing | run |

Version: Sept 25, 2010

passband end frequency, attenuation, transformation of $H(s)$ to $H(z)$, bilinear or impulse invariance.nb | .cdf | listing |

report | run |

Version: July 5, 2011

Simulation of Computed Tomography (CT), Radon transform. Incremental angle version.nb | .cdf | listing | run |

Version: July 4, 2011

Simulation of Computed Tomography (CT), Radon transform. Incremental angle version.nb | .cdf | listing | run |