algorithm - What are possible methods for creating a physical engine -

this general question comes answer issue interests me general knowledge , not answer specific problem.

i wondering available ways implement physical engine objects interact each other , outside forces. example can @ angry birds, or games tim. there objects "fly" through air, collide , interact each other, , affected potential of environment gravity, winds , other "forces".

the model have thought each object has object (as object of class) , thread relate it. each time slot thread "advances" object in space small dt. in case have "environment" object can position in space , give equivalent force applied environment potential. can't how objects interact each other?

also, close in direction? there other solutions , models problems, , better? things i'm missing (i must missing things)?

the implementation typically nothing describe, way expensive. instead, reduced matrix transformations. points lists of coordinates operated on matrices update them next time interval. matrices calculated physics (they linear solution of forces @ moment, more or less).

things more complicated when have large differences in scale (say, simulating stars in galaxy). may use more hierarchical approach critical (eg fast moving or, more accurately, accelerating) points updated more non-critical points. in-memory representation abstract , nothing direct "one object per thing".