There are two sorts of hopping.
One where the outside wheel is gripping, releasing and gripping again and one where the inside wheel is gripping, releasing and gripping again.
The outside problem is caused by the adhesion between track and road breaking down, because you have exceeded either the mechanical limit or the chemical limit. What tends to happen is that you are loading up the wheel, the grip fails catastrophically releasing the load on the wheel and then the wheel comes under load again until the grip breaks again.
The solution is to change whatever is causing the break away, so that the grip fails in a predictable manner rather than catastrophically. If the problem is chemical grip, (ie: the tyres are too sticky) then you alter the stickiness, if the problem is mechanical, then alter the contact patch
Hopping on the inside wheel is caused by the inside wheel having too much grip, and the 'easy' solution is mechanical, lift the wheel.
The problem though is usually a combination and the difficulty comes from combining both solutions. There's no point in lifting the inside wheel if that reduces the outer contact patc and switches from hopping on the inside to hopping on the outside or vice versa.
So: harder axle and drive it through the corner will solve inside hopping by lifting the wheel, while a softer, shorter axle will present a different contact patch on the outer wheel. Both are right for different situations.
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