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Symmetry

Hey guys,

Can you please help me .

My question is "Why symmetry leads to stability?"

Note by Rithik Sharma
1 year, 10 months ago

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This is a totally wide open, undefined question, but I'll answer it anyway! Let's say that "tendency to change" is some function of some parameter, $$f\left(x\right)$$. If, for some value $$x$$, there is a symmetry about it, i.e.,$$f\left( x-\Delta x \right) =f\left( x+\Delta x \right)$$, then it's a extremum, and so it could either be a point of stability or instability. Like a bowl, which could be inverted. Even when it's inverted, it doesn't necessarily mean it'll move---it first has to be knocked off center. The point is, at the extremum, there is no "tendency to change". · 1 year, 10 months ago

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Thank u guys · 1 year, 10 months ago

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Where? In what situation? Unless you give us some more detail, any answers will probably be too general to be useful. · 1 year, 10 months ago

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Sure. Think of a boat in water. Boats are usually symmetrical along the center vertical plane. · 1 year, 10 months ago

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