Guide
1
itself given vector does nothing in terms of the mathematical description of the motion, so it is considered in the projections on the coordinate axes.This may be one coordinate axis (beam), two (plane) or three (space).To find the projection, you need to drop a perpendicular from the end of the vector along the axis.
2
Projection is like a "shadow" of the vector.If the body is moving perpendicular to the axis of projection degenerate to the point and will have a value of zero.When moving parallel to the coordinate axis projection coincides with the unit vector.And when the body moves so that its velocity vector is directed at an angle φ to the axis x, the projection on the x-axis is the segment: V (x) = V • cos (φ), where V - velocity module.The projection is positive
when the direction of the velocity vector coincides with the positive direction of the coordinate axis, and negative in the opposite case.
3
Let the motion of a point set coordinate equations: x = x (t), y = y (t), z = z (t).Then a function of speed, projected on the three axes will have the form, respectively, V (x) = dx / dt = x '(t), V (y) = dy / dt = y' (t), V (z) =dz / dt = z '(t), that is, to find the speed needed to take derivatives.Self velocity vector will be expressed by the equation V = V (x) • i + V (y) • j + V (z) • k, where i, j, k - the unit vectors of the coordinate axes x, y, z.Unit rate can be calculated by the formula V = √ (V (x) ^ 2 + V (y) ^ 2 + V (z) ^ 2).
4
Through the direction cosines of the velocity vector and the unit interval of the coordinate axes, you can set the direction of the vector, throwing his unit.For a point which moves in a plane just two coordinates, x and y.If the body makes circular motion, the direction of the velocity vector is constantly changing, and the module can either be kept constant, and change over time.