Physics Simulations

Click on one of the physics simulations below... you'll see them animating in real time, and be able to interact with them by dragging objects or changing parameters like gravity. You'll need to get Java software to view the simulations, if you don't already have it.

single spring
single spring
double spring
double spring
pendulum
pendulum
pendulum with direction field
pendulum with
direction field
chaotic pendulum
chaotic pendulum
2 chaotic pendulums
2 chaotic pendulums
moveable pendulum
moveable pendulum
double pendulum
double pendulum
moveable double pendulum
moveable double
pendulum
inverted vibrating pendulum
inverted vibrating
pendulum
inverted double pendulum
inverted double
pendulum
2D spring
2D spring
double 2D spring
double 2D spring
colliding blocks
colliding blocks
cart with pendulum
cart with pendulum
dangling stick
dangling stick
rigid body collisions
rigid body
collisions
rigid body with contact forces
rigid body with
contact forces
roller coaster
roller coaster
roller coaster with spring
roller coaster
with spring
roller coaster with 2 balls
roller coaster
with 2 balls
roller coaster with flight
roller coaster
with flight
Brachistochrone
The Brachistochrone:
fastest slide path
Billiards
Billiards /
Air Hockey
Chain
Hanging Chain
Newtons Cradle
Newtons Cradle
molecule 2
molecule 2
molecule 3
molecule 3
molecule 4
molecule 4
molecule 5
molecule 5
molecule 6
molecule 6

How Does It Work?

Explanations of the math and physics are provided in the simulation web pages. Free source code is provided for those wanting to experiment on their own. Here are some additional pages about the underlying math and software.

Help and FAQ How to get the simulations to work, and other answers.
Differential Equations Intro A gentle introduction to differential equations
Classifying Differential Equations A taxonomy of differential equations
Numerical Solutions How to solve a differential equation with a computer
Runge Kutta Method Commonly used method for numerically solving differential equations
Math Refresher For those whose trig and calculus are a wee bit rusty.
Collision Handling Methods Discusses various schemes for handling collisions in rigid body simulations.

Why Physics Simulation?

These physics simulations can be used to: Simulations are essential in many areas of science and engineering. When problems become more complex, it is difficult to use pure math techniques to predict what will happen. Scientists and engineers then create a mathematical model and use numerical techniques to run the model on a computer.

Also of Interest

Links to related math, physics, and simulation websites.
Displaying Math on the Web Notes about how to display mathematics on the web.
Gladtex is software for displaying LaTeX mathematics in a web page.
FunctionLab, is a graphing calculator which can graph up to 4 functions at once.

About The Author

Erik Neumann photo Hi, my name is Erik Neumann, I live in Seattle, WA, USA, and I am a self-employed software engineer. I started developing this website in 2001, both as a personal project to learn scientific computing, and with a vision of developing an online science museum. I grew up in Chicago near the Museum of Science and Industry which I loved to visit and learn about science and math.

I got a BA in Mathematics at Oberlin College, Ohio, 1978, and an MBA from Univerity of Chicago, 1984. My first software jobs were using the language APL which I enjoyed for it's math-like conciseness and power.

I was fortunate to get involved in the Macintosh software industry early on in 1985, joining MacroMind, which became Macromedia. I led the software development at MacroMind as VP of Engineering for 5 years. Our most significant product was VideoWorks, which was renamed Director, and lives on today as Adobe Director. In the 1980's, the interactive multimedia concepts that are so common today were new and being developed. VideoWorks was mainly an animation tool, but also incorporated programmable interactivity. Our main competitors at that time were HyperCard, SuperCard, and Authorware. Director was used in many different ways; I am most proud that it became the preferred way to prototype software user interfaces for a time during the 90's. Director was also used to develop the introductory "guided tour" tutorial that came with the Macintosh in the early years. And of course, Director was used for all sorts of art, design, and marketing projects.

I went on to work at Apple Computer on new multimedia and user interface concepts involving digital agents, animated user interfaces, speech recognition and distributed information access. In 1991, there was a sudden flurry of activity when Apple and IBM were trying to set up a strategic partnership. I became involved in the super-secret negotiations, and made the suggestion that what the world needed was a standard for multimedia that multimedia content creators could rely on to publish to (ultimately this is what HTML became). Based on these suggestions, Kaleida Labs was founded. Our work there developed a product called ScriptX, which turned out to be very similar to Sun's Java which was being developed at the same time. ScriptX had goals of supporting all forms of multimedia: text, images, audio, video, animation; being cross-platform (Mac and Windows), interpreted, object oriented, with a garbage collector to manage memory.

I then moved to Seattle and turned my attention back to mathematics and science. I relearned calculus by doing all the problems in my old college text book and took further math classes at the University of Washington. I started developing this website as a way to practice what I was learning. I am now happy to use excellent tools such as HTML and Java, and leave their development to others. I continue to work on physics simulations, with several new ones in development.




This web page was first published April 2001.

Valid HTML 4.01!