The goal is to have a generic driving module that can have adjustable parameters (such as velocity and acceleration) to meet different profiles ( so I suppose the second option that you listed). But this driver won't be used for a robot arm, it will just be used for positioning (however, if you...
yes, those are the correct numbers. Here is a another plot showing when the pulses become constant and the total 'ramp up time'
As far as the physical hardware, this is actually a simulation of stepper driver module that is running on a Cyclone 10 FPGA which is sending the pulses to a stepper...
Hi Berkeman,
Yes, this is from a logic analyzer simulation that is counting steps from a stepper motor (each pulse is one step). And yes, the numbers on the bottom are keeping track of how many pulses have occurred. I should have mentioned that the horizontal axis is time.
Also yes, my goal is...
Hello,
Perhaps I am overthinking this, but I am trying to find the acceleration of the 'pulse rate' in the below plot.
Every so many seconds there is a pulse (you can think of this as x displacement). The initial rate between pulses is 5 pulses/sec (you can think of this as velocity). I am...
Ok, so I figured it out:
If you have a DE system that is linear, then if we know eigenvalue and eigenvectors of a coefficient matrix A, we know that trajectory plots starting at the ends of the eigenvectors will be:
{x1[t_], y1[t_]} = eigenvector[1] E^(eigenvalue[1] t)
{x2[t_], y2[t_]} =...
Ok, so this is a differential equation question.
How can I use the eigenvectors/eigenvalues to find the formulas for straight line trajectories and from those formulas that I come up with, how can I alter them so as to start at any given point that I would like them to (like with starter data)...
Well, I want to say that:
C1 Cos(5t) + C2 Sin(5t) = C1 Cos(5t) + C2 Sin(kt)
and that k is just 5.
Is that right to say?
I'm asking this not because I have trouble determining if k = 5, but mainly to make sure I did my work correct in finding
C1 Cos(5t) + C2 Sin(5t)
then I know that k = 5...
oh ok.
One final question regarding this.
When I switch up the constants, I get
C1 Cos(5t) + C2 Sin(5t)
But, I'm suppose to come up with
C1 Cos[5 t] + C2 Sin[k t]
So what should I do about that k? Why is it not a 5? Or does k have to equal 5?
Thanks.
-James
Ok, I guess it's my constants that are getting me in a twist.
Where am I going wrong here?
knowing that:
E^(ix) = cos(x) + i sin(x)
and
E^(-ix) = cos(x) - i sin(x)
K1 E^(-5 i t) + K2 E ^(5 i t)
(Let x = 5t)
= K1 (cos(x) - i sin(x)) + K2(cos(x) + i sin(x))
= cos(x) (K1 + K2) + i sin(x)...
Homework Statement
Given:
y''[t] + 25 y[t] = 0
I know that the solution to this DE is of the form:
y[t] = K1 E^(-5 i t) + K2 E ^(5 i t)
I get that, that makes sense to me, however when I look in old DE books I see the solution to the same problem written as:
C1 Cos[5 t] + C2...
So sorry! made a big bobo!
I want to show:
.5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t) = Sin(pi t/4)
Using the above does just that.
Thanks so much! :)
Ok, so I have
.5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t)
knowing:
E^(i theta) = cos(theta) + i sin(theta)
E^(-i theta) = cos(theta) - i sin(theta)
so
.5 i E^(i theta) = .5 i (cos(theta) + i sin(theta)) = .5 (i cos(theta) - sin(theta))
.5 i E^(i -theta) = .5 i (cos(theta) - i sin(theta)) =...
Ok,
E^(i theta) - E^(-i theta) = 2 i sin(theta)
I'm still a little bit confused as to where I can go from this.
I like the way the right hand side of the equation is looking, but I don't know what to do with the imaginary component in 2 i sin(theta)
Thanks,
-James
Homework Statement
Hello,
I am in differential equations currently and I have a homework question regarding simplifying
sin( Pi t)/4
into
.5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t)
Homework Equations
I think they might be using Euler's Identity, but I am unsure.
E^(a +...