Conservative force is gradient of potential energy¶
A conservative force is a such a force, the total work of which in moving a particle between two points is independent of the path taken. Alternative definition states that if a particle travels in a closed loop, the total work done by a conservative force is zero.
Conditions:
Force is conservative. Mathematically, this can be expressed as \(\text{curl} \, {\vec F} \! \left( \vec r \right) \equiv 0\), i.e. the force field must be irrotational.
Links:
- position_vector¶
Position vector of a point in space. See
distance_to_origin.
- Symbol:
r- Latex:
\({\vec r}\)
- Dimension:
length
- force¶
Vector field of the conservative force as a function of the :attr`position_vector`. See
force.
- Symbol:
F(r)- Latex:
\({\vec F} \left( {\vec r} \right)\)
- Dimension:
force
- potential_energy¶
Scalar field of the force’s potential as a function of the :attr`position_vector`. See
potential_energy.
- Symbol:
U(r)- Latex:
\(U{\left({\vec r} \right)}\)
- Dimension:
energy
- law¶
F(r) = -grad(U(r))- Latex:
- \[{\vec F} \left( {\vec r} \right) = - \text{grad} \, U{\left({\vec r} \right)}\]