Scratch

Actually, switch the sin and cos functions used to compute vx1 and vy1, and see how that works...

chalkmarrow wrote:

Actually, switch the sin and cos functions used to compute vx1 and vy1, and see how that works...

If I did that then Vy would have a value when it is pointing straight down and Vx would have a value if the pendulum is horizontal.

I have just created a project that simulates a pendulum.
http://scratch.mit.edu/projects/archmage/128694

You can check it out if you want. There isn't a lot of code in it.

You never said you wanted a double pendulum. Are you going to use this for anything specific?

archmage wrote:

You never said you wanted a double pendulum. Are you going to use this for anything specific?

Possibly for my next science fair project.

Oh, like this?

http://scratch.mit.edu/projects/Mayhem/129626

Yep. That's a pretty non-linear system. I'd be impressed if someone could simulate that in Scratch such that it actually runs at a reasonable rate. The matrix method is pretty straightforward, so that might be a good start...

Well, this is the closest I can get to one:
http://scratch.mit.edu/projects/thecooltodd/131516

lol

Thanks.  I found several websites like that as well.  How fast could scratch calculate these though?
θ1'' =        −g (2 m1 + m2) sin θ1 − m2 g sin(θ1 − 2 θ2) − 2 sin(θ1 − θ2) m2 (θ2'2 L2 + θ1'2 L1 cos(θ1 − θ2))
L1 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))
θ2'' =       2 sin(θ1 − θ2) (θ1'2 L1 (m1 + m2) + g(m1 + m2) cos θ1 + θ2'2 L2 m2 cos(θ1 − θ2))
L2 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))

thecooltodd wrote:

Thanks.  I found several websites like that as well.  How fast could scratch calculate these though?
θ1'' =        −g (2 m1 + m2) sin θ1 − m2 g sin(θ1 − 2 θ2) − 2 sin(θ1 − θ2) m2 (θ2'2 L2 + θ1'2 L1 cos(θ1 − θ2))
L1 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))
θ2'' =       2 sin(θ1 − θ2) (θ1'2 L1 (m1 + m2) + g(m1 + m2) cos θ1 + θ2'2 L2 m2 cos(θ1 − θ2))
L2 (2 m1 + m2 − m2 cos(2 θ1 − 2 θ2))

As g, and the mass of the two pendulems, and the lengths are constant, you can simplify the equations a lot before putting them into scratch.

EG, taking G as 10, and both pendulems as mass 1 and length 1, you get:

θ1'' =        −30 sin θ1 − 10 sin(θ1 − 2 θ2) − 2 sin(θ1 − θ2) 10 (θ2'2 + θ1'2 cos(θ1 − θ2))
(3 − cos(2 θ1 − 2 θ2))L1 (3 − cos(2 θ1 − 2 θ2))
(I think)

(though shouldn't there be a "t" for time in there somewhere?)

Anyways, does anyone understand the Lagrangian equation?  Because actually I believe I may be able to simplify (by my definition of simplify) the overall angular acceleration equation.  But I need to be sure how to use Lagrangian equations to do that...

I haven't been checking the website for a while and Chalkmarrow pointed me to this thread.

Regarding time.  Normally in physics simulations you don't have to calculate the second derivative because you don't do the simulations using absolute time, it's normally done using delta times.  Then you only calculate the movement made during that delta time.

Is this just to do a simulation or is it to create an equation for the path of the pendulums?  If it is just for simulation I would do it using impulses and moments of inertia.  Then it wouldn't matter how many pendulums were linked to one another.  I think I will take a look at that approach some time today.