Dave Mac wrote:On the other hand, Rainmaker is spot on with Calculus of Manifolds methodolgy ~ this being employed within Euclidian Space Theory. It is better treated with differentiable manifolds ~ these are embedded within Euclidian Space, and are at a level that can be understood by many.
Moreover, a differentiable manifold is a topological manifold. In addition, it is more common to define Euclidean space using Cartesian coordinates, eminently suitable for describing ski turns in a geometrical situation.
So, well done Rainmaker on that one.
Thats exactly what I worked on during my season in Soldeu. Although I did alternate between Euclidian and Bacchanalian Space!!!
First one typo, Calculus of Manifolds, is known in its simpler forms (and it is not simple) as Calculus of Variations. Yes, while the basic Brachistochrone Curve solution is based on a frictionless surface, it is valid for surfaces with friction too, but introduction of friction creates many other complications, basically everything leads to fluid dynamical system like pde's and so small variations can lead to big changes in the solution. Also, the solution is deeper and holds even when there is an initial velocity different from zero.
Point I was trying to contribute in this discussion was simple:
(a) straight line representing shortest distance down a slope is NOT the fastest way
(b) world class and other good racers know that, and find that cycloidal path, friction and all, not always perfect but they know, that is what they train for, and that is how they find the "thin line".
(c) there is a reason when one watches racers closely, depending on the race, i.e. GS, vs Downhill vs. Slalom and all that, you can see where they turn high and early, and in other cases turn very late using pivot transitions etc.
Am not expert by the way, and I never read that article referenced by some dude earlier but now I have, and I thank you for it, good piece for sure. Not all correct, but not a bad effort, since the entire enterprise is an inexact, hard to define problem.
And again, I am not an expert.
Am not expert by the way, and I never read that article referenced by some dude earlier
And again, I am not an expert.
If you want to refer to a post by another forum member, it's useful to use their Forum name. It's on their post.
I am quite proud of myself for finding that article, based on Brodie's PhD thesis. I'm glad you found it interesting
I couldn't get the link to work and SwingBeep very kindly fixed it for me:
SwingBeep wrote:And there was me naively thinking I was the only one barmy enough to read scientific literature on skiing.
AllyG, unfortunately the link is broken.
Have to say some of terms seemed pretty confusing. Either my understand was incorrect or they have changed from what I have been taught. Is "Lateral projection", the extension of the weighted ski during carving?
Pumping I didn't fully understand, although seems to relate to bringing skis back underneath body, which related closely to above?
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