183_notes:force_and_pe

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183_notes:force_and_pe [2021/04/01 12:50] – [Equilibrium Points] stumptyl183_notes:force_and_pe [2023/11/30 20:35] (current) – [Force is the Negative Gradient of Potential Energy] hallstein
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 To find the force in three-dimensions, this derivative of the potential becomes the [[http://en.wikipedia.org/wiki/Gradient|gradient]] of the potential, To find the force in three-dimensions, this derivative of the potential becomes the [[http://en.wikipedia.org/wiki/Gradient|gradient]] of the potential,
  
-$$\vec{F} = - \nabla U = \left\langle \dfrac{dU}{dx},  -\dfrac{dU}{dy},  -\dfrac{dU}{dz}\right\rangle$$+$$\vec{F} = - \nabla U = \left\langle -\dfrac{dU}{dx},  -\dfrac{dU}{dy},  -\dfrac{dU}{dz}\right\rangle$$
 $$\vec{F} = -\dfrac{dU}{dx}\hat{x} -\dfrac{dU}{dy} \hat{y} -\dfrac{dU}{dz} \hat{z}$$ $$\vec{F} = -\dfrac{dU}{dx}\hat{x} -\dfrac{dU}{dy} \hat{y} -\dfrac{dU}{dz} \hat{z}$$
  
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  • Last modified: 2021/04/01 12:50
  • by stumptyl