Mathematica Scientiﬁc Demonstrations
by Nasser M. Abbasi. Updated April 1, 2015
These are Mathematica demos I wrote over the last 3 or so years. Some of these are also published at Wolfram demonstration web site The Mathematica CDF plugin needs to be installed in your browser to run any of these CDF demos. The plugin is free and easy to install from Wolfram CDF plugin webpage.
1 Equation of motion simulation of RRR robot arm in 3DLast changed: April 1, 2015 Equations of motion of 3 degrees of freedom robot arm (3 revolute joints) is derived and simulated. You can adjust the torque at each joint, and add damping and initial angles.
The derivation is PDF and notebook

2 Kharitonov triangle for interval polynomialLast changed: Nov 28, 2014 Simulation of motion of Kharitonov triangle for using two intervals polynomial as illustrations

3 Simple example of 3D rotationLast changed: April 8, 2015 Cube is rotated in 3D

4 Showing basic use of Radon/Inverse radon transformsLast 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

5 Wave equation using leap frogLast 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.

6 Symmetric top gyro motionLast changed: July 15, 2014 Adjust the initial wheel spin for symmetric gyro top and watch the eﬀect on motion.

7 Eﬀect on precession due to spinning wheelLast 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

8 Spinning wheelLast changed: June 29, 2014 Adjust the radius, number of rods and angle to see the wheel spin in 3D

9 Rotation stability of 3D cubeLast 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.

10 Rotation stability of cylinderLast changed: June 28, 2014 Cylinder is a solid object which has one unique moment of inertia, which is around the zaxis. When it is spinning around zaxis, 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.

11 simple springmassdamper simulationLast changed: June 19, 2014 Change the mass, stiﬀness or damping and see the eﬀect on motion of mass. No stop bar case.

12 simple springmassdamper with stopbarLast 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.

13 three pendulums with two springsLast 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.

14 Simulation of rigid body dynamicsLast changed: Dec 19, 2013 Final project EMA 542. Two noncollinear rotating bodies

15 Another rigid body dynamicsLast changed: Dec 19, 2013 A small simulation, Solving EMA 542 HW3 problem 1

16 Direct and Shear Strain Deformation in 3DLast 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)

17 Finite Diﬀerence FormulasLast changed: August 29, 2013 Generated By Interpolating Polynomial. Shows error in approximation based on which formula used

18 2D rectangular membrane modal analysisLast changed: July 31 2013 PDE solved is Where is the amplitude of the wave

19 Generalized Single Degree Of Freedom MethodLast 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

20 Vibration analysis of forced single degree freedom systemLast changed: August 29 2013 Solving vibration, resonance, critical damping, beat beat phenomenon, impulse response, magniﬁcation factor

21 Vibration analysis of free unforced single degree freedom systemLast changed: July 24 2013 Solving vibration system.

22 Velocity and acceleration components for circular motionLast 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.

23 Adding Gaussian noise to signal using SNRLast 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.

24 elliptical satellite motion demoLast changed: January 24, 2014 Change the ellipse eccentricity and see the eﬀect on motion of satellite.

25 Double pendulum using heavy springLast changed: January 18, 2015 Three degrees of freedom, Lagrangian method, Rayleigh factor, eﬀective weight of spring

26 particles collision simulationLast changed: Sept 25, 2012 collision detection using priori (continuous) detection. Supports up to 8 particles.

27 Spring Mass System On a Rotating TableLast changed: August 8, 2012 moment of inertia, rotation dynamics, springmass on spinning disk

28 Triple pendulum with dampingLast changed: September 1, 2011 Triple, double and simple pendulum, damped medium. Lagrangian. phase portrait

29 Chaotic motion of damped driven pendulumLast changed: September 2, 2011 Bifurcation, Poincare map, Power Spectrum, Phase Portrait

30 Mass on a spring at end of a solid pendulumLast changed: Nov 10, 2012 Lagrangian method, spring mass, NDSolve

31 Rigid body disk pendulum rotating on moving tableLast changed: June 25, 2011 Lagrangian, principal moments of inertia, angular momentum dL/dt, 3 nonlinear equations of motion, numerical solution with NDSolve

32 Rigid body pendulum on a ﬂywheelLast 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

33 Direct dynamics for simulation of pendulumLast changed: Nov 10, 2012 simulation of damped and driven pendulum with chaotic motion using direct Dynamics without using Manipulate

34 cylinders with 3 springsLast changed: July 26,2013 Simulation of motion of 2 masses connected by 3 springs. Equations derived using the Lagrangian energy method

35 LQR Control of inverted pendulum on moving cartLast changed: April 16, 2012 Simulation of LQR control

36 PID controller design for second order systemLast changed: Feb 2, 2012 P, PI, PD, or PID. simulate the plant with and without the controller, Bode, Nyquist, open and closed loop

37 Mohr's Circle For Plane Stress, 2DLast changed: Nov 10, 2013 principle stresses and Mohr's Circle

38 Single span Euler Bernoulli beamLast changed: Oct 21 2009 deﬂection curve of beam, bending moment, shear diagrams, point load, distributed load, external moment, deﬂection ratio

39 ﬁnite element Ritz method for axially loaded beamLast changed: 6/2/2012 deﬂection curve of beam, bending moment, shear diagrams, point load, distributed load, external moment, deﬂection ratio

40 Solving 2D Poisson PDE on nonuniform rectangle gridLast changed: May 30, 2014 2D Poisson PDE on nonuniform rectangle grid. . Neummann, Dirichlet B.C. direct, Jacobi, GaussSeidel, GaussSeidel red/black, SOR, Chebyshev, steepest descent, conjugate gradient, GMRES, BiCGSTAB, sparse matrices

41 solving Helmholtz diﬀerential equation in 2D using ﬁnite diﬀerenceLast changed: Feb 2, 2012 solving Helmholtz diﬀerential equation in 2D. Dirichlet, Sommerfeld B.C. in 2D, Dirichlet, Sommerfeld B.C.

42 solving Helmholtz diﬀerential equation in 1D using ﬁnite diﬀerenceLast changed: March 6, 2012 solving in 1D, Dirichlet, Sommerfeld B.C.

43 Solving diﬀusionadvectionreaction (heat) in 1DLast changed: Feb 20, 2012 solving in 1D. Neummann, Dirichlet B.C.

44 Finite diﬀerence solution of the diﬀusionconvection in 1DLast changed: Feb 10, 2012 solving in 1D, Dirichlet, Neummann B.C.

45 Minimal example to solve Poisson 2D using Jacobi methodLast changed: March 6, 2012 Illustrate Jacobi method

46 Finite diﬀerence for solving Poisson PDE on unit squaredLast changed: Nov 14, 2010 small example, numerical solution of Poisson PDE on unit square. Dirichlet B.C. on unit square, Dirichlet B.C.

47 Design a digital ﬁlter by geometric meansLast changed: April 12 2009 select poles and zero locations with mouse, magnitude spectrum, BodePlot, Stability Margins, Nyquist, Nichols, root locus, Splane map,region of convergence, convert to

48 From continuoustodiscrete time Fourier transform by samplingLast 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

49 Fourier series coeﬃcients of a rectangular pulse signalLast changed: April 12 2009 plot magnitude and phase of the Fourier coeﬃcients for a rectangular pulse train signal, sinc function

50 Phase plane plot of the Van der Pol diﬀerential equationLast changed: April 12 2009 phase plot vs. , Van der Pol nonlinear diﬀerential equation for diﬀerent initial conditions

51 Analogtodiscrete system conversion using impulse invarianceLast changed: May 3, 2010 Applied to second order system, sampling, poles, zeros. ,

52 ImageData using rows and columnsLast changed: August 7, 2013 Change image size using matrix notation

53 Power eﬃciency of amplitude modulationLast changed: August 31 2009 Illustrates the eﬀect of changing the modulation factor on the power eﬃciency of ordinary amplitude modulation (AM)

54 Rectangular pulse and its Fourier transformLast changed: December 27 2009 Manipulate a rectangular pulse signal and observe how its Fourier transform changes

55 sinc interpolation to reconstruct a signal from its sampleLast changed: Feb 18 2010 sinc interpolation

56 Power content of frequency modulation and phase modulationLast changed: September 6 2009 BesselJ, modulation index, carrier frequency, carrier amplitude, deviation constant, bandwidth of the modulated carrier, power ratio.

57 IIR digital lowpass Filter Design by Butterworth methodLast changed: Sept 25, 2010 passband end frequency, attenuation, transformation of to , bilinear or impulse invariance

58 Computed tomography using Radon Transform (incremental angles)Last changed: July 5, 2011 Simulation of Computed Tomography (CT), Radon transform. Incremental angle version

59 Computed tomography using Radon TransformLast changed: July 4, 2011 Simulation of Computed Tomography (CT), Radon transform. Incremental angle version

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

61 Illustrating the use of discrete distributions in Version 7Last changed: December 28, 2013 The probability mass function and the cumulative distribution function are displayed for all Mathematica 7 discrete distributions


