|May8-12, 08:09 PM||#1|
Angular and Linear Velocities to position
Hello everyone. First of all, thank you for any help you can provide.
The essence of the problem is this. I am given the linear and angular velocity of an object at a given moment in time.
Data looks like this:
Time(s): Linear velocity (m/s) Angular velocity(rad/s)
10.313 0.075 0.241
Given the previous position (in x/y cooridnates) and orientation (angle in radians), and this information, I want to calculate the new position and orientation 0.1 seconds later.
Equations I've been using:
radius of turning = linear velocity/angular velocity
change in theta = angular velocity * timestep(0.1 seconds)
x-coordinate = r*cos(theta)
y-coordinate = r*sin(theta)
I realized that we don't really know whether the object will be moving about a circle to its left, or a circle to its right (i.e. is angular velocity clockwise or counter clockwise). I decided to pick one and stick with it, to see how it went.
I'm programming in MATLAB, so here is the code for the function I've written:
function [newx newy neworient] = newstate(l_vel, ang_vel, tstep, old_orient, old_x, old_y) r = (l_vel/ang_vel); del_orient = ang_vel * tstep; neworient = old_orient + del_orient; center_x = old_x - r*cos(neworient); center_y = old_y - r*sin(neworient); newx = center_x + r*cos(del_orient); newy = center_y + r*sin(del_orient); end
Again, thank you all for any help.
|May8-12, 08:31 PM||#2|
If I am following your question, you are trying to find the position of the particle in rectangular coordinates after .1 second.
I am assuming the velocity given is the tangential velocity and the particle is moving in a circle. You can easily find the radius of the circle if you know Vt and ω. You need to set up a rectangular coordinate system. Let say the radius lays along the x-axis, so the particle at time t=0 sec is (r,0). Using rotational motion equations you can find the angle of rotation after 0.1 second. Since you know the radius and angle use basis trig to find the coordinates of the new position. It probably be helpful if you draw the problem out.
|angular velocity, linear velocity, matlab, position|
|Similar Threads for: Angular and Linear Velocities to position|
|Transformation of angular and linear velocities (to determine dynamics of an object)||General Physics||0|
|Transformation of angular and linear velocities||Differential Geometry||0|
|Conserved angular momentum: finding angular velocities of drums as a function of time||Introductory Physics Homework||2|
|Getting the magnitude of linear acceleration from angular position equation||Introductory Physics Homework||6|
|Post collision angular and linear and velocities of a rotating sphere||Classical Physics||5|