Physics Dynamics

[Yahaira Petrov]

Notethe text of this page is from my original website, and I haven't updated it in a while. Make sure you look at the physics category for all of the articles related to rigid body dynamics.

I started getting interested in high end physical simulation for gamessometime in 1995. Since I didn't know anything about physics or knowany real math (I had calculus in high school and enjoyed it, but hadforgotten most of it), I had to teach myself everything from scratch.Let me just say it was a total blast. I highly recommend everyonetaking the time to learn something really big and new every once in awhile, in addition to all the little things we're all [hopefully]learning every day. As a bonus, it seems that the more we learn, thefaster we're able to learn even newer things, which makes the wholeprocess even more pleasurable.

As much fun as I had figuring this stuff out, I sure would haveappreciated some references and articles aimed at my level when I wasstarting. So, I've created this web page in the hopes I can helpeveryone else get past those difficult first steps.

I wrote a total of four articles about rigid body dynamics for Game Developer Magazine. I've posted them as PDF files, so theylook just like they do in the magazine. There are downsides to PDF,however, including the general way in which Acrobat sucks at lettingyou navigate through documents (it's clear Adobe thinks a monitor is alowres printer), and perhaps more seriously, the way some of theequations came out garbled. However, you should think of the latterproblem as a challenge to figure out the correct equations! [Ifpeople complain enough I'll figure out how to fix them.] Pleaserespect the copyright information in the front of each article.

Four articles, no matter how long, are just not enough to do justiceto rigid body dynamics. If you plan on using real dynamics in yourgame, you simply have to read my Physics References. The3D sample application below shows the beginnings ofsome really cool technology, but you'll have to take the initiative toteach yourself more math and physics to turn it into a production qualitysimulator.

Remember, these are just sample programs, not the ultimate physicssimulators. They're really just a translation of the equations in myarticles into code, so don't expect too much. They're fun to playwith and change, but you'll have a lot of your own work to do beforeyou can use this stuff in a production quality game. These apps willget you started, but not much more than that.

The most obvious thing the samples are missing is inter-body collisions. They don't do collision detection between bodies, but only betweenbodies and the world. It wouldn't be too hard to add a very simplediscrete collision detector, but I didn't have time.

The second biggest problem is the lame integrator used in both apps.Both samples are relatively unstable because I'm using the simplestEuler integrator. If you play with the spring and dampingcoefficients you'll quickly see how tweaky they are with relation tothe timestep with this cheesy integrator. There are tons of books on numerical integration to helpyou fix this problem.

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Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

I am trying to pick a physics engine for a simple software application. It would be to simulate a rather small number of objects so performance isn't a huge concern. I am mostly concerned with the accuracy of the motion involved. I would also like the engine to be cross-platform between windows/linux/mac and usable with c++ code. I was looking at Bullet, Newton Game Dynamics, and ODE because they are open source. However, if Havok/PhysX are significantly more accurate I would consider those too.

All I seem to find are opinions on the engines, are there any thorough comparisons between the options? Or does anyone have experience trying the various engines out. Since what I'm trying to do is relatively simple there probably isn't a huge difference between them, but I'd like to hear what people have to say about the options? Thanks!

Sorry, but you will never find a real comparison with respect to accuracy. I am searching for three months now for my master thesis and have not found it. So I started to do the comparison on my own but it's still a long way to go. I'm testing with 3d engines and even 2d engines and for now Chipmunk is the one with the highest accuracy so far. So if you have no need for 3d I would reccomend it. However if you have an urgent need for 3d and your problem is as simple as you described it (don't want to expand it in the future?) Bullet and ODE will do it. I would prefer Bullet because it is much more up-to-date and is still actively maintained. At least there is Newton, with which I am fighting right now. Therefore I can't give you pros and cons except that it is a bit more work to get familiar with the (crucial) bad documentation.Hope that helps. Best regards.

One thing I found really valuable in ODE is the ability to change pretty much every single parameter 'on the fly'. As an example, the engine doesn't seem to complain if you modify the inertia or even the shape of a body. You could replace a sphere with a box and everything would just keep working, or change the size of the sphere.Other engines are not as flexible usually, because they do a lot of work internally for optimization purposes.As for accuracy, as far as I know, ODE still supports a very accurate (but slow) solver which is obviously not very popular in the games industry because you can't play around with more than 25-30 objects in real time. Hope this helps.

Check out Simbody, which is used in engineering. It's particularly good for simulating articulated bodies. It has been used for more than 5 years to simulate human musculoskeletal dynamics. It's also one of the physics engines used in Gazebo, a robot simulation environment.

A physics abstraction layer supports a large number of physics engines via a unified API, making it easy to compare engines for your situation.PAL provides a unique interface for these physics engines:

Of the open source engines the Bullet engine provided the best results overall, outperforming even some of the commercial engines. Tokamak was the most computationally efficient, making it a good choice for game development, however TrueAxis and Newton performed well at low update rates. For simulation systems the most important property of the simulation should be determined in order to select the best engine.

Dynamics is the branch of physics and mechanical engineering that deals with the motion and forces of objects and systems. It involves the study of how objects move and interact with each other under the influence of different forces and energies.

Dynamics is used in various real-world applications, such as designing vehicles, analyzing the motion of machines and structures, and understanding the behavior of fluids and gases. It is also essential in fields like robotics, aerospace engineering, and biomechanics.

The key principles of dynamics include Newton's laws of motion, the conservation of energy, and the conservation of momentum. These principles help us understand and predict the motion of objects and systems in different situations.

Statics deals with the analysis of objects and systems at rest or in equilibrium, while dynamics focuses on objects and systems in motion. In other words, statics involves the study of forces acting on stationary objects, while dynamics involves the study of forces causing objects to move or change their motion.

Dynamics is closely related to other branches of physics, such as kinematics, mechanics, and thermodynamics. It also has applications in various fields of engineering, including civil, mechanical, and aerospace engineering. Understanding dynamics is essential for solving complex problems and designing efficient systems in these fields.

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Photons do not easily interact with one another. This property is commonly exploited to communicate over long distances using optical fibres. Interaction between photons is desired, however, for classical and quantum information processing, but requires a highly nonlinear medium. Optical nonlinear processes are employed in a range of photonic applications such as frequency conversion, optical modulation, light amplification and sensing1,2,3. In the limit where the optical nonlinearity is expressive on the scale of a few photons, one can observe quantum nonlinear phenomena, for instance via the optical correlation functions3,4,5. One manifestation of the nonlinearity is the presence of two- and higher-order photon bound states. Photons in these bound states are strongly correlated, such that the likelihood of observing a photon at any one time is fixed, but once one photon is detected, the arrival of another is much more likely than at a random time. We emphasise that photon bound states are distinct from bunched photon states, as photon bound states are quasiparticles that have their own dispersion relation and are eigenstates of the underlying Hamiltonian that describes the nonlinear medium. It has recently been predicted theoretically that the photon-number-dependent propagation velocity of photon bound states can lead to the formation of highly entangled, ordered states of light6. Photon bound states have been predicted to exist in a number of systems, such as unidirectional waveguide quantum electrodynamics (QED)7,8,9 and strongly correlated Rydberg gases10. In the latter case, experimental observations consistent with their presence have been reported11,12,13. A direct observation of their dynamics is, however, lacking. To observe directly the dynamics of photon bound states, we examine the unidirectional propagation of few-photon wavepackets strongly interacting with a single atom, in practice a semiconductor quantum dot (QD) coupled to a one-sided cavity.

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