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Two-dimensional elastic collision. In a center of momentum frame at any time the velocities of the two bodies are in opposite directions, with magnitudes inversely proportional to the masses. In an elastic collision these magnitudes do not change. The directions may change depending on the shapes of the bodies and the point of impact.
The degree of relative kinetic energy retained after a collision, termed the restitution, is dependent on the elasticity of the bodies‟ materials.The coefficient of restitution between two given materials is modeled as the ratio [] of the relative post-collision speed of a point of contact along the contact normal, with respect to the relative pre-collision speed of the same point along the ...
The collision detection algorithm doesn't need to understand friction, elastic collisions, or worse, nonelastic collisions and deformable bodies. In addition, the a posteriori algorithms are in effect one dimension simpler than the a priori algorithms. An a priori algorithm must deal with the time variable, which is absent from the a posteriori ...
The COR is a property of a pair of objects in a collision, not a single object. If a given object collides with two different objects, each collision has its own COR. When a single object is described as having a given coefficient of restitution, as if it were an intrinsic property without reference to a second object, some assumptions have been made – for example that the collision is with ...
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
Collision detection may be discrete/a posteriori (meaning objects are advanced in time through a pre-determined interval, and then any penetrations detected and resolved), or continuous/a priori (objects are advanced only until a collision occurs, and the collision is handled before proceeding). The former is easier to implement and faster, but ...
For identical elastic balls of any type with initially touching balls, the action is the same for the first strike, except the time to complete a collision increases in softer materials. Forty to fifty percent of the kinetic energy of the initial ball from a single-ball strike is stored in the ball surfaces as potential energy for most of the ...
The Verlet integration would automatically handle the velocity imparted by the collision in the latter case; however, note that this is not guaranteed to do so in a way that is consistent with collision physics (that is, changes in momentum are not guaranteed to be realistic). Instead of implicitly changing the velocity term, one would need to ...