4 ms·
No, it is not. I can not exactly pin down where the mistake in the linked paper is after looking at it for five minutes but I am pretty sure it is related to hi
by danbruc 10y ago
No, it is not. I can not exactly pin down where the mistake in the linked paper is after looking at it for five minutes but I am pretty sure it is related to his choice of r(t) in equation 4 as a piecewise polynomial so that a t = T there is a discontinuity in the 4th derivative which is non-physical, i.e. without a force tangential to the dome at the apex the object would never move away from the apex of the dome. If you only look at lower order derivatives like velocity and acceleration, then there is no discontinuity and everything seem superficially fine.
- kurthr 10y agoI agree, this is likely a joke paper. I find it fairly hilarious since at it looks like the standard Divide by Zero algebra problem, but then error after error compounds the result. The first error appears to be in an un-numbered equation: sin(theta)=dh/dr which is equal to 0 at r=0!! which is then substituted into the differential equation: F=g dh/dr = sqrt(r) = d^2r/dt^2 again equal to ZERO at r=0 Of course this is also an abuse of Leibniz notation (mathematicians squirm whenever physicists do this sort of "algebra" on differentials) which is then integrated twice and then differentiated twice (ignoring constants of integration) to get the equations for r(t) and a(t). The second key is the square root, which allows for multiple solutions of the differential equation (one of which is the normal r=a=0), but that's just part of the side show. Physics has all sorts of "non-physical" results from integrations, DiffEq, etc. A classic being a negative time solution to parabolic trajectories. I would add the use the statistics of continuos probability distributions to say that there is in fact ZERO probability that any ball is at r=0 just to complete the silliness. Perhaps he's willing to co-author a follow up?