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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.
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 ...
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.. In the simplest case of circular motion at radius , with position given by the angular displacement () from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: =.
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative ...
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.
Timing diagram over one revolution for angle, angular velocity, angular acceleration, and angular jerk. Consider a rigid body rotating about a fixed axis in an inertial reference frame. If its angular position as a function of time is θ(t), the angular velocity, acceleration, and jerk can be expressed as follows:
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.