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Numerical integration and collision detection

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Im developing a framework for rigid body simulations and in the process of implementing a couple of collision detection algorithms. Before i start implementing i have some troubles on my mind. For example with the RK4 method i calculate four deratives and then the weighted average for each object and i was starting to wonder were the collision detection step would fit in. In order to retain the accuracy of the RK4 i guess you should do the collision check with each Derative you calculate but wouldn´t that cause strange things to happen? For example if you apply a thrust to the left to two objects which are positioned side by side eachother and then do the integration. When you calculate the second Derative for the first object(first object is on the right side) and integrate the position for that Derative the object may intersect the second. When you check for collision for the second derative for the first object a collision will be found and the object will be moved and forces recalculated but that is not the result you want because you haven´t integrated the second object yet and it will move in the same direction so no collision will occour. Does anyone have any solutions to my problems?

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