Path/time function of a freesbie (the ride at amusement parks)

[haruspex]

Assume the usual (?) units, so w (omega) in angle/time, time in s, and angles in angles.

No, you can't do that. If you only have symbolic inputs to work with then the answer is symbolic and does not use or need units.
If you are told a car travels at speed v for time t then the distance covered is vt, not vt miles or km or light years.
If you are told it travels at v km/h for 10 minutes then answer is v/6 km.
If told it travels at speed v for n hours then the answer is vn hours (really!).
The units in the answer come from the inputs, nowhere else.

 

[Kakainsu]

By writing it as a cross product, yes: e→s=e→R×e→ϕ, say.
So now you want to express a vector that rotates steadily in the e→s,e→ϕ plane.

No, you can't do that. If you only have symbolic inputs to work with then the answer is symbolic and does not use or need units.
If you are told a car travels at speed v for time t then the distance covered is vt, not vt miles or km or light years.
If you are told it travels at v km/h for 10 minutes then answer is v/6 km.
If told it travels at speed v for n hours then the answer is vn hours (really!).
The units in the answer come from the inputs, nowhere else.

If you actually differntiate, which Acceleration do you get? The acceleration vectors in a_1, a_2, a_3 direction, which are caused by the motion of the freesbie? And then, what acceleration of forces do we need to add on top of that? The Gravitational force? The force that compensates the gravitational force? What other forces do I have to consider?

 

[haruspex]

If you actually differntiate, which Acceleration do you get?

If you have a vector expression for the location of the person at time t, relative to some fixed point, then differentiating that twice with respect to t will give you the acceleration vector in the ground frame.
There will be no need to consider forces.

 

[Kakainsu]

If you have a vector expression for the location of the person at time t, relative to some fixed point, then differentiating that twice with respect to t will give you the acceleration vector in the ground frame.
There will be no need to consider forces.

From my understanding, we now have an expression for the person at time t. I'm still very unsure of how I can differntiate this equation. Because everything will be in terms of the unit vectors. So how do I get there? I tried to differntiate, which was really messy and probably is pretty wrong, but the thing that annoys me the most: how do I actually get to the acc, even if I have values for w_1 (the one for the vertical swing) and w_2 (for the circular motion? Btw I have angle Phi for vertical swing and theta for circular.

 

[haruspex]

From my understanding, we now have an expression for the person at time t. I'm still very unsure of how I can differntiate this equation. Because everything will be in terms of the unit vectors. So how do I get there? I tried to differntiate, which was really messy and probably is pretty wrong, but the thing that annoys me the most: how do I actually get to the acc, even if I have values for w_1 (the one for the vertical swing) and w_2 (for the circular motion? Btw I have angle Phi for vertical swing and theta for circular.

You don't seem to have understood my post #27.
You need to write the unit vectors as functions of time, using the knowledge that the pendulum will be executing SHM. Then you can differentiate wrt time.

 

[Kakainsu]

You don't seem to have understood my post #27.
You need to write the unit vectors as functions of time, using the knowledge that the pendulum will be executing SHM. Then you can differentiate wrt time.

How can I write unit vectors as functions of time?

 

[haruspex]

How can I write unit vectors as functions of time?

You have (x , y) vectors for them in terms of $\phi$, and you can get $\phi$ as a function of t from the SHM equation.

 

[Kakainsu]

You have (x , y) vectors for them in terms of $\phi$, and you can get $\phi$ as a function of t from the SHM equation.

So phi = w*t?

But how can I go on from there? I mean i don't know how to differentiate this...can you maybe give me an example of how you would differntiate the circular motion with changing planes, so expressed by e_phi and e_s? I'd be super happy, I really want to understand it but its hard

 

[haruspex]

So phi = w*t?

No, it is a pendulum. For small swings, it will be something like $\phi=\phi_{max}\sin(\omega_p t)$. To get $\dot\phi$, just differentiate that.
Note that $\omega_p$ is unrelated to the $\omega$ we introduced for the uniform rotation of the Frisbee about its axis.

 

[Kakainsu]

No, it is a pendulum. For small swings, it will be something like $\phi=\phi_{max}\sin(\omega_p t)$. To get $\dot\phi$, just differentiate that.
Note that $\omega_p$ is unrelated to the $\omega$ we introduced for the uniform rotation of the Frisbee about its axis.

Could you please be so kind and differentiate the path/time function twice? I know it's a lot but I just don't get it.

 

[haruspex]

Could you please be so kind and differentiate the path/time function twice? I know it's a lot but I just don't get it.

First, we have to get that function in terms of t and constants. I have given you the general form of the function for the pendulum angle. From that, obtain the function for the position of the Frisbee's centre.
Post what you get.