Difference between revisions of "Forest UCM Energy CurlFcons"

From New IAC Wiki
Jump to navigation Jump to search
Line 5: Line 5:
 
=Definition of curl=
 
=Definition of curl=
  
W have seen that the garden operator is defined in cartesian coordinates as
+
We have seen that the gradient operator is defined in cartesian coordinates as
  
 
:<math>\vec \nabla = \frac{\partial}{\partial x} \hat i +\frac{\partial}{\partial y} \hat j +\frac{\partial}{\partial z} \hat k</math>
 
:<math>\vec \nabla = \frac{\partial}{\partial x} \hat i +\frac{\partial}{\partial y} \hat j +\frac{\partial}{\partial z} \hat k</math>
 +
 +
can be used to find the function form of a conservative force given its potential energy
  
 
[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]]
 
[[Forest_UCM_Energy#Second_requirement_for_Conservative_Force]]

Revision as of 23:09, 23 September 2014

A force with a curl of zero is a conservative force.

Thus taking the curl of the force is an easier way to test for conservative forces rather than calculating the work and inspecting to see if it only depends on the endpoints of the motion.

Definition of curl

We have seen that the gradient operator is defined in cartesian coordinates as

[math]\vec \nabla = \frac{\partial}{\partial x} \hat i +\frac{\partial}{\partial y} \hat j +\frac{\partial}{\partial z} \hat k[/math]

can be used to find the function form of a conservative force given its potential energy

Forest_UCM_Energy#Second_requirement_for_Conservative_Force