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Symmetry

Hey guys,

Can you please help me .

My question is "Why symmetry leads to stability?"

Note by Rithik Sharma
2 years, 1 month 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".

Michael Mendrin - 2 years, 1 month ago

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Thank u guys

Rithik Sharma - 2 years, 1 month 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.

Raj Magesh - 2 years, 1 month ago

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Sure. Think of a boat in water. Boats are usually symmetrical along the center vertical plane.

Michael Mendrin - 2 years, 1 month ago

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