Motion of a Particle in Space
In a Nut Shell: A particle can be located by its position vector, r, in space. Description
of its motion involves both its velocity vector, v, and its acceleration vector, a .
Let r = (x, y, z) be a position vector from the origin, O, to an arbitrary point P(x,y,z)
(particle) on a curve, C, in space . Then dr / dt is a vector tangent to this curve.
This curve, C, represents the path of motion of the particle, P, in space.
dr / dt also represents the velocity of the particle along its path
where r = x i + y j + z k where i , j, k are unit vectors (base vectors)
along axes x, y, and z fixed in space (using a rectangular, Cartesian description).
Here x = x(t), y = y(t), and z = z(t) t = time
So v = dr / dt = dx/dt i + dy/dt j + dz/dt k
where dx/dt, dy/dt, and dz/dt represent the x, y, and z-components of velocity
of the particle moving along C.
Acceleration of a particle in space – using “rectangular” Cartesian (x,y,z) components
Acceleration of a particle is the time rate of change of its velocity, v = dr / dt .
So a = dv / dt . In “rectangular coordinates” x, y, z
a = dv / dt = d2x/dt2 i + d2y/dt2 j + d2z/dt2 k
Copyright © 2011 Richard C. Coddington
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