Thread: derivatives of vector functions

first bit done stuck on second part:

The equations of motion of a point particle in space are given by

1. x(t) = 2t^3 - 3, y(t)= -3t^3, z(t)= 4t^3 - 1

2. x(t)= asin(wt), y(t) = acos(wt), z(t) = t

In each case, calculate the velocity vector v and the acceleration vector a. Also, calculate the absolute values of these vectors.

Now the bit I can't do is,

what are the curves along which the particle moves?
(find these values for an arbitraryt, with a and w being fixed parameter)

Originally Posted by sonia1

first bit done stuck on second part:

The equations of motion of a point particle in space are given by

1. x(t) = 2t^3 - 3, y(t)= -3t^3, z(t)= 4t^3 - 1

2. x(t)= asin(wt), y(t) = acos(wt), z(t) = t

In each case, calculate the velocity vector v and the acceleration vector a. Also, calculate the absolute values of these vectors.

Now the bit I can't do is,

what are the curves along which the particle moves?
(find these values for an arbitraryt, with a and w being fixed parameter)

.... (1)

.... (2)

.... (3)

From (1), (2) and (3) it follows that the path is a line with cartesian equation


.... (1)

.... (2)

(1) + (2): .

You have a spiral with a circular cross-section centred along the z-axis.

could you please show me a sketch of what it actually looks like