Re:Uncontrollability of a bricycle (2014) [video]
by tzs on Wednesday April 18, 2018 @11:14AM
(#16868032)
> But try this: Try following a straight marker on the road on your bike. It's very hard. When you start going too much to the right, you will find it impossible to actually nudge the bike back to the left, unless you accept that you have to go further to the right first.
This holds in general for any motion where velocity is a continuous function of time, doesn't it?
Let f(t) be your deviation at time t perpendicular to the desired straight path, with positive to the right and negative to the left.
If you are "going too much to the right" at time t, e.g., f'(t) > 0, then because f' is continuous there must be some interval around t such that f' > 0 at all points in the interval. That means that f is strictly increasing throughout that interval, e.g., "you have to go further to the right first".
This holds in general for any motion where velocity is a continuous function of time, doesn't it?
Let f(t) be your deviation at time t perpendicular to the desired straight path, with positive to the right and negative to the left.
If you are "going too much to the right" at time t, e.g., f'(t) > 0, then because f' is continuous there must be some interval around t such that f' > 0 at all points in the interval. That means that f is strictly increasing throughout that interval, e.g., "you have to go further to the right first".