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Related Concept Videos

Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
Elastic Collisions: Introduction01:00

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
Ellipses01:30

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest diameter,...
Types of Collisions - II01:19

Types of Collisions - II

When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...
Collisions in Multiple Dimensions: Introduction01:05

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Types Of Collisions - I01:04

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When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...

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Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
09:44

Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System

Published on: June 5, 2014

Continuous collision detection for ellipsoids.

Yi-King Choi1, Jung-Woo Chang, Wenping Wang

  • 1Department of Computer Science, The University of Hong Kong, Hong Kong. ykchoi@cs.hku.hk

IEEE Transactions on Visualization and Computer Graphics
|January 17, 2009
PubMed
Summary
This summary is machine-generated.

We developed an efficient algorithm for continuous collision detection between two moving ellipsoids. This method accurately identifies collision time intervals for rational Euclidean or affine motion, enhancing robotic and physics simulations.

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Area of Science:

  • Computational geometry
  • Robotics
  • Computer graphics

Background:

  • Continuous collision detection is crucial for realistic simulations.
  • Existing methods for ellipsoidal collision detection can be computationally intensive.
  • Ellipsoids are common shapes in physics-based simulations and robotics.

Purpose of the Study:

  • To develop an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids.
  • To handle rational Euclidean or affine motion.
  • To determine precise time intervals of collision.

Main Methods:

  • An optimized interference testing algorithm for stationary ellipsoids was adapted.
  • An algebraic condition based on the characteristic equation of two ellipsoids was utilized.
  • A time-dependent characteristic equation was derived for moving ellipsoids.

Main Results:

  • The algorithm accurately detects collisions between moving ellipsoids.
  • It efficiently computes the specific time intervals during which collisions occur.
  • Demonstrated effectiveness through practical examples.

Conclusions:

  • The proposed algorithm offers an accurate and efficient solution for continuous collision detection of moving ellipsoids.
  • This method can significantly improve the performance of simulations involving dynamic ellipsoidal objects.
  • The approach is suitable for applications requiring real-time collision analysis.