1 Kharitonov triangle for interval
polynomial
Last changed: Nov 28, 2014

Simulation of motion of Kharitonov
triangle for using two
intervals polynomial as illustrations

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2 Wave equation using leap frog
Last changed: July 5, 2014

Solve wave equation
using leap frog method. boundary
conditions are ﬁxed on left and right
side. Initial speed is zero. Select initial
data and see the wave move.

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3 Showing basic use of
Radon/Inverse radon transforms
Last changed: Sept 22, 2014

Select the Radon transform method
and the inverse Radon transform ﬁlter
and change the cut oﬀ frequency and
see the eﬀect on the image

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4 Wave equation using leap frog
Last changed: July 5, 2014

Solve wave equation
using leap frog method. boundary
conditions are ﬁxed on left and right
side. Initial speed is zero. Select initial
data and see the wave move.

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5 Symmetric top gyro motion
Last changed: July 15, 2014

Adjust the initial wheel spin for
symmetric gyro top and watch the
eﬀect on motion.

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6 Eﬀect on precession due to
spinning wheel
Last changed: June 29, 2014

Modify the wheel spin rate, its radius
and distance from the support and see
the eﬀect on the precession spin rate

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7 Spinning wheel
Last changed: June 29, 2014

Adjust the radius, number of rods and
angle to see the wheel spin in 3D

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8 Rotation stability of 3D cube
Last changed: 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.

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9 Rotation stability of cylinder
Last changed: 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.

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10 simple spring-mass-damper
simulation
Last changed: June 19, 2014

Change the mass, stiﬀness or damping
and see the eﬀect on motion of mass.
No stop bar case.

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11 simple spring-mass-damper with
stopbar
Last changed: 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.

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12 three pendulums with two
springs
Last changed: 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.

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13 Simulation of rigid body
dynamics
Last changed: Dec 19, 2013

Final project EMA 542. Two
noncollinear rotating bodies

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14 Another rigid body dynamics
Last changed: Dec 19, 2013

A small simulation, Solving EMA 542
HW3 problem 1

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15
Direct and Shear Strain Deformation
in 3D
Last changed: 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)

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16 Finite Diﬀerence Formulas
Last changed: August 29, 2013

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

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17 2D rectangular membrane modal
analysis
Last changed: July 31 2013

PDE solved is
Where is the amplitude of
the wave

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18 Generalized Single Degree Of
Freedom Method
Last changed: 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

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19 Vibration analysis of forced
single degree freedom system
Last changed: August 29 2013

Solving
vibration, resonance, critical damping,
beat beat phenomenon, impulse
response, magniﬁcation factor

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20 Vibration analysis
of free unforced single degree freedom
system
Last changed: July 24 2013

Solving
vibration system.

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21 Velocity and acceleration
components for circular motion
Last changed: 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.

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22 Adding Gaussian noise to signal
using SNR
Last changed: 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.

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23 elliptical satellite motion demo
Last changed: January 24, 2014

Change the ellipse eccentricity and see
the eﬀect on motion of satellite.

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24 Double pendulum using heavy
spring
Last changed: January 18, 2015

Three degrees of freedom, Lagrangian
method, Rayleigh factor, eﬀective
weight of spring

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25 particles collision simulation
Last changed: Sept 25, 2012

collision detection using priori
(continuous) detection. Supports up to
8 particles.

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26 Spring Mass System On a
Rotating Table
Last changed: August 8, 2012

moment of inertia, rotation dynamics,
spring-mass on spinning disk

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27 Triple pendulum with damping
Last changed: September 1, 2011

Triple, double and simple pendulum,
damped medium. Lagrangian. phase
portrait

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28 Chaotic motion of damped driven
pendulum
Last changed: September 2, 2011

Bifurcation, Poincare map, Power
Spectrum, Phase Portrait

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29 Mass on a spring at end of a solid
pendulum
Last changed: Nov 10, 2012

Lagrangian method, spring mass,
NDSolve

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30 Rigid body disk pendulum
rotating on moving table
Last changed: June 25, 2011

Lagrangian, principal moments of
inertia, angular momentum dL/dt,
3 nonlinear equations of motion,
numerical solution with NDSolve

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31 Rigid body pendulum on a
ﬂywheel
Last changed: 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

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32 Direct dynamics for simulation
of pendulum
Last changed: Nov 10, 2012

simulation
of damped and driven pendulum with
chaotic motion using direct Dynamics
without using Manipulate

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33 cylinders with 3 springs
Last changed: July 26,2013

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

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34 LQR Control of inverted
pendulum on moving cart
Last changed: April 16, 2012

Simulation of LQR control

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35 PID controller design for second
order system
Last changed: Feb 2, 2012

P, PI, PD, or PID. simulate the plant
with and without the controller, Bode,
Nyquist, open and closed loop

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36 Mohr's Circle For Plane Stress,
2D
Last changed: Nov 10, 2013

principle stresses and Mohr's Circle

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37 Single span Euler Bernoulli beam
Last changed: Oct 21 2009

deﬂection curve of beam, bending
moment, shear diagrams, point load,
distributed load, external moment,
deﬂection ratio

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38 ﬁnite element Ritz method for
axially loaded beam
Last changed: 6/2/2012

deﬂection curve of beam, bending
moment, shear diagrams, point load,
distributed load, external moment,
deﬂection ratio

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39 Solving 2D Poisson PDE on
non-uniform rectangle grid
Last changed: May 30, 2014

2D Poisson PDE on non-uniform
rectangle grid. .
Neummann, Dirichlet B.C. direct,
Jacobi, Gauss-Seidel, Gauss-Seidel
red/black, SOR, Chebyshev, steepest
descent, conjugate gradient, GMRES,
BiCGSTAB, sparse matrices

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40 solving Helmholtz diﬀerential
equation in 2D using ﬁnite diﬀerence
Last changed: Feb 2, 2012

solving Helmholtz diﬀerential
equation in 2D. Dirichlet, Sommerfeld
B.C. in 2D,
Dirichlet, Sommerfeld B.C.

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41 solving Helmholtz diﬀerential
equation in 1D using ﬁnite diﬀerence
Last changed: March 6, 2012

solving in 1D,
Dirichlet, Sommerfeld B.C.

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42
Solving diﬀusion-advection-reaction
(heat) in 1D
Last changed: Feb 20, 2012

solving in
1D. Neummann, Dirichlet B.C.

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43 Finite diﬀerence solution of the
diﬀusion-convection in 1D
Last changed: Feb 10, 2012

solving in 1D,
Dirichlet, Neummann B.C.

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44 Minimal example to solve
Poisson 2D using Jacobi method
Last changed: March 6, 2012

Illustrate Jacobi method

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45 Finite diﬀerence for solving
Poisson PDE on unit squared
Last changed: Nov 14, 2010

small example, numerical solution of
Poisson PDE on unit square. Dirichlet
B.C. on
unit square, Dirichlet B.C.

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46 Design a digital ﬁlter by
geometric means
Last changed: 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 to

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47 From continuous-to-discrete
time Fourier transform by sampling
Last changed: April 7 2010

Relation between continuous time
Fourier transform (CTFT)
of a continuous time signal
and discrete time Fourier transform
(DTFT) of the discrete signal
sampling

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48 Fourier series coeﬃcients of a
rectangular pulse signal
Last changed: April 12 2009

plot magnitude and phase of the
Fourier coeﬃcients for a rectangular
pulse train signal, sinc function

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49 Phase plane plot of the Van der
Pol diﬀerential equation
Last changed: April 12 2009

phase plot vs. , Van der
Pol nonlinear diﬀerential equation for
diﬀerent initial conditions

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50 Analog-to-discrete system
conversion using impulse invariance
Last changed: May 3, 2010

Applied
to second order system, sampling,
poles, zeros. ,

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51 ImageData using rows and
columns
Last changed: August 7, 2013

Change image size using matrix
notation

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52 Power eﬃciency of amplitude
modulation
Last changed: August 31 2009

Illustrates the eﬀect of
changing the modulation factor on the
power eﬃciency of ordinary amplitude
modulation (AM)

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53 Rectangular pulse and its
Fourier transform
Last changed: December 27 2009

Manipulate a rectangular pulse signal
and observe how its Fourier transform
changes

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54 sinc interpolation to reconstruct
a signal from its sample
Last changed: Feb 18 2010

sinc interpolation

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55 Power content of frequency
modulation and phase modulation
Last changed: September 6 2009

BesselJ, modulation index, carrier
frequency, carrier amplitude, deviation
constant, bandwidth of the modulated
carrier, power ratio.

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56 IIR digital low-pass Filter Design
by Butterworth method
Last changed: Sept 25, 2010

passband end frequency, attenuation,
transformation of to ,
bilinear or impulse invariance

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57 Computed tomography using
Radon Transform (incremental angles)
Last changed: July 5, 2011

Simulation of Computed Tomography
(CT), Radon transform. Incremental
angle version

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58 Computed tomography using
Radon Transform
Last changed: July 4, 2011

Simulation of Computed Tomography
(CT), Radon transform. Incremental
angle version

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59 Illustrating the use of discrete
distributions in Version 8
Last changed: Oct 18, 2014

Illustrating the use of discrete
distributions in Version 8.

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60 Illustrating the use of discrete
distributions in Version 7
Last changed: December 28, 2013

The probability mass function and
the cumulative distribution function
are displayed for all Mathematica 7
discrete distributions

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