Search results
Results from the WOW.Com Content Network
For example, to calculate the dynamics of a billiard ball being struck, one can approximate the force of the impact by a Dirac delta. In doing so, one not only simplifies the equations, but one also is able to calculate the motion of the ball, by only considering the total impulse of the collision, without a detailed model of all of the elastic ...
Delta-v is typically provided by the thrust of a rocket engine, but can be created by other engines. The time-rate of change of delta-v is the magnitude of the acceleration caused by the engines, i.e., the thrust per total vehicle mass. The actual acceleration vector would be found by adding thrust per mass on to the gravity vector and the ...
The delta potential is the potential = (), where δ(x) is the Dirac delta function. It is called a delta potential well if λ is negative, and a delta potential barrier if λ is positive. The delta has been defined to occur at the origin for simplicity; a shift in the delta function's argument does not change any of the following results.
The longer it can accelerate its own mass, the more delta-V it delivers to the whole system. In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant.
Jump-discontinuity in acceleration can be modeled using a Dirac delta function in jerk, scaled to the height of the jump. Integrating jerk over time across the Dirac delta yields the jump-discontinuity. For example, consider a path along an arc of radius r, which tangentially connects to a straight line. The whole path is continuous, and its ...
Another generalization of the Laplace operator that is available on pseudo-Riemannian manifolds uses the exterior derivative, in terms of which the "geometer's Laplacian" is expressed as =. Here δ is the codifferential, which can also be expressed in terms of the Hodge star and the exterior derivative. This operator differs in sign from the ...
The generalized Kronecker delta or multi-index Kronecker delta of order is a type (,) tensor that is completely antisymmetric in its upper indices, and also in its lower indices. Two definitions that differ by a factor of p ! {\displaystyle p!} are in use.
velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian heat capacity ratio: unitless surface tension: newton per meter (N/m) delta: change in a variable (e.g. ) unitless Laplace operator: per square meter (m −2)