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Trajectory of a particle with initial position vector r 0 and velocity v 0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t. The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical ...
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 ...
However, closed-form time-independent path equations of an elliptic orbit with respect to a central body can be determined from just an initial position and velocity (). For this case it is convenient to use the following assumptions which differ somewhat from the standard assumptions above:
The velocity equation for a hyperbolic trajectory is = ... the satellite's initial position and velocity vectors and at a given epoch =. In a two-body simulation ...
This is the equation of a parabola, so the path is parabolic. The axis of the parabola is vertical. If the projectile's position (x,y) and launch angle (θ or α) are known, the initial velocity can be found solving for v 0 in the afore-mentioned parabolic equation:
Velocity is the speed in combination with the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it.
These equations may be solved ... is the initial velocity ... which is like using a frame of reference with constant translational velocity. Indeed, to derive the ...
The meaning of the constants and can be easily found: setting = on the equation above we see that () =, so that is the initial position of the particle, =; taking the derivative of that equation and evaluating at zero we get that ˙ =, so that is the initial speed of the particle divided by the angular frequency, =.