OK, you have the acceleration of the bucket. You still need another differential equation for how the water flows out the orifice on the bottom. The water will flow out faster when the bucket is accelerating upwards and flow out slower when the bucket is decelerating. You still need two...
What confuses me, actually it is the rest of you that are confused, is that your $$x_f = x_i+v_i*(t_f- t )+(1/6)*j*(t_f - t )^3$$ equation shows that x_f and x_i are constants but then the times should be constants too such as (t_f-t_i) . (t_f-t_i) is a ##\Delta t##. There should be no...
Which kinematic equation do you want to derive? There are lots of them! What I have seen above is that people don't even know how to integrate or differentiate.
Most of the time you know the initial position, velocity and acceleration and you want to move to another position, velocity and...
You need to solve two differential equations simultaneously. One models the water flowing from the cup and the other models the position of the cup. Use Runge-Kutta to solve numerically.
##\Delta t## can be negative. The trick part calculating the coefficients and it seems people have a hard time doing that. If you assume ##\Delta t## can be negative then it is possible to calculate a position, velocity and acceleration before time 0 for that particular polynomial. Notice...
No, my post #21 was accurate. There have been too many posts that don't show basic knowledge of a third order equation applied to motion or even how to integrate and differentiate basic polynomials. My link above shows how it is done. Now do you want to dispute what I posted in #27 ?
You...
This is the blind leading the blind. I write code for motion controllers and sell them around the world.
Below is A SIMPLE example of using seven third order polynomials to make a whole motion from one point to another.
https://deltamotion.com/peter/wxMaxima/Seg1234567.html
The code is here...
I don't agree with the at_f(t_f-t) part.
##\Delta x=v\cdot\Delta t+\frac{a\cdot\Delta t^2}{2}##
Get a program that can integrate and differentiate polynomials.
wxMaxima will do.
So what ball is ideal? I would think a table tennis ball is pretty close to ideal. They are relatively smooth and seamless. A table tennis ball wouldn't be so far off from ideal that the Magnus force is 10+ times higher than it should be.
All the equations that are valid ( the units are...
This is basically the same simulation as before using the NASA formula. The acceleration due to the Magnus effect is still way too high.
I am not simulating a serve. I am simulating a loop where the ball is it at a height 50mm about the table so the ball must be hit up to go over the net and...
What do you mean by a short fraction of a second? If the acceleration due to the Magnus effect is 1.48N and mass is only 2.7gm the ball will take off. This It will accelerate up or down exceesively depending on the direction of spin.
Are you sure? Have you EVER seen this equation used in a...
This still doesn't work. Although the formula results in units of force, the magnitude of the lift is too great.
I use b=0.0205 m for the radius of a 40+ TT ball. I use 25 rev/sec for s ( spin ) and 17 m/sec for the velocity V.
Notice that NASA specifies the spin in revolution per second as...
Formula looks correct except it doesn't say what S0, the Magnus coefficient, is. This coefficient is the key. This document is like all the others. They have no idea what the Magnus coefficient is.
I simulated a golf drive using data I got off the internet but using the same Mathcad equations and a Cm of 0.29 which seems too high for a table tennis ball but about right for a golf ball.
I am simulating a pro drive. A pro can hit the ball at 180 mph. The optimal angle is 16 degrees. The...
It is easy to do what you ask. I can just set Cd and Cm to 0. The ball flies past the end of the able.
The Cm, Magnus coefficient, plays a much bigger part in landing the ball than the drag. I see nothing unexpected as long as I set Cm to 0.05 instead of 0.29 as in the document. Wikipedia...