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t 1 and t 2 are times when the impulse begins and ends, respectively, m is the mass of the object, v 2 is the final velocity of the object at the end of the time interval, and; v 1 is the initial velocity of the object when the time interval begins. Impulse has the same units and dimensions (MLT −1) as momentum.
For a free, rigid beam, an impulse is applied at right angle at a point of impact, defined as a distance from the center of mass (CM). The force results in the change in velocity of the CM, i.e. d v c m {\displaystyle dv_{cm}} :
Einstein Triangle. The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc 2 relates total energy E to the (total) relativistic mass m (alternatively denoted m rel or m tot), while E 0 = m 0 c 2 relates rest energy E 0 to (invariant) rest mass m 0.
Delta-v (also known as "change in velocity"), symbolized as and pronounced /dɛltə viː/, as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or landing on a planet or moon, or an in-space orbital maneuver.
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to be equivalent to units of speed; this interpretation is commonly labeled the effective exhaust velocity. If a force-based unit system is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
α is the angle of attack; m is the vehicle's mass; D is the vehicle's aerodynamic drag; L is its aerodynamic lift; r is the radial distance to the planet's center; and; g is the gravitational acceleration at altitude. Mass decreases as propellant is consumed and rocket stages, engines or tanks are shed (if applicable).