A link to the Tokamak Physics SDK Docs :
http://www.tokamakphysics.com/documentation/
A link to the Home Page :
http://www.tokamakphysics.com/index.htm
And a link to the WIKI :
http://en.wikipedia.org/wiki/Tokamak_physics_engine
Here is a link to another Physics Engine SDK that is free(Open Source) called ODE - Open Dynamics Engine, its specifically for rigid body physics.
http://www.ode.org/ode.html
and some tutorials for ODE :
http://www.alsprogrammingresource.com/ode.html
And lastly, another Free Phsics engine, this one specifically for games - Newton Game Dynamics
http://newtondynamics.com/forum/newton.php
As for tutorials on integrating it with DarkGDK I am sorry to say that is something you will have to figure out on your own as I dont know of any. There are some wrappers for DarkBasic Pro using ODE and Tokamak and also Newton Game Dynamics I believe, you can find them by searching the forums, perhaps their author's may be able to help you more with integration.
That is, im afraid to say, the drawback of the "free alternative", it generally requires alot more work to get going than the same or similar things that you can purchase... ( Im not saying that you should purchase products if you dont want to or cant afford to, just that its generally the easier option )
Anyway, if you do end up trying to integrate one of the above engines, I wish you the best of luck, and look forward to seeing the results
If it ain't broke.... DONT FIX IT !!!