FOWLES CASSIDAY 4.2

1. 1
2
3
, det min
:
(a)
(b) -
(c)
By finding the curl er e
which of the following forces
are conservative
ix jy kz
iy jx kz
iy jx kz
  
 
  
F
F
F
Solution
Conservative Field
In summary, the curl of a conservative force
field is zero everywhere because a field being
conservative is equivalent to having zero curl,
which can be derived in any basic text on
vector analysis. Additionally, a conservative
force field can be written as the gradient of a
scalar field.

2. 2
2 3
4
( )
( 1) 0 ( 1) 0
( 1) 0 0
Conservative
a
i j k
X
x y z
x y z
i X j X
k X
  

  
    
 

 F

3. 3
2
2 3
4
( )
( 1) 0 ( 1) 0
( 1) ( 1 1) 2 0
Not Conservative
b
i j k
X
x y z
y x z
i X j X
k X
  

  

    
     

 F
3
2 3
4
( )
( 1) 0 ( 1) 0
( 1) (1 1) 0
Conservative
c
i j k
X
x y z
y x z
i X j X
k X
  

  
    
  

 F
Analytical Mechanics Grant R. Fowles George L. Cassiday