1 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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2 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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3 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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4 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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5 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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6 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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7 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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8 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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9 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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10 Simulation of rigid body
dynamics
Last changed: Dec 19, 2013

Final project EMA 542. Two
noncollinear rotating bodies

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

A small simulation, Solving EMA
542 HW3 problem 1

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12 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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13 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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14 2D rectangular membrane
modal analysis
Last changed: July 31 2013

PDE solved is
Where is the amplitude
of the wave

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15 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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16 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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17 Vibration analysis of free
unforced single degree freedom
system
Last changed: July 24 2013

Solving
vibration system.

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18 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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19 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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20 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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21 Double pendulum using heavy
spring
Last changed: Sept 10, 2012

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

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22 particles collision simulation
Last changed: Sept 25, 2012

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

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23 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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24 Triple pendulum with
damping
Last changed: September 1, 2011

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

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

Bifurcation, Poincare map, Power
Spectrum, Phase Portrait

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

Lagrangian method, spring mass,
NDSolve

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27 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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28 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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29
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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30 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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31 LQR Control of inverted
pendulum on moving cart
Last changed: April 16, 2012

Simulation of LQR control

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32 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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33 Mohr's Circle For Plane
Stress, 2D
Last changed: Nov 10, 2013

principle stresses and Mohr's Circle

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34 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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35 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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36 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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37 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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38 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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39 Solving
diﬀusion-advection-reaction (heat)
in 1D
Last changed: Feb 20, 2012

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

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40 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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41 Minimal example to solve
Poisson 2D using Jacobi method
Last changed: March 6, 2012

Illustrate Jacobi method

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42 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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43 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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44 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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45 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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46 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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47 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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48 ImageData using rows and
columns
Last changed: August 7, 2013

Change image size using matrix
notation

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49 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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50 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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51
sinc interpolation to reconstruct a
signal from its sample
Last changed: Feb 18 2010

sinc interpolation

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52 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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53 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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54 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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55 Computed tomography using
Radon Transform
Last changed: July 4, 2011

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

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56 Illustrating the use of discrete
distributions in Version 8
Last changed: September 1, 2008

Illustrating the use of discrete
distributions in Version 8.

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57 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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