Mixing
Difference between right-differential and left-differential gradients
$begingroup$
Studying Continuum Mechanics with Capaldi's book [1, p.27], he states that
the gradient can each be expressed in terms of a vector differential operator named the Del operator, which is defined in Cartesian coordinates as either a right-differential operator, $overrightarrow{nabla}$,or left-differential operator,$overleftarrow{nabla}$. The direction of the arrow signifies the direction in which the operator acts, according to the book.
Does anybody have a clue on what do they mean with the "direction which the operator acts"?
[1] Capaldi, Franco. 2012. Continuum Mechanics : Constitutive Modeling of Structural and Biological Materials. Cambridge, MA: Cambridge University Press.
vector-analysis
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
$endgroup$
add a comment |
$begingroup$
Studying Continuum Mechanics with Capaldi's book [1, p.27], he states that
the gradient can each be expressed in terms of a vector differential operator named the Del operator, which is defined in Cartesian coordinates as either a right-differential operator, $overrightarrow{nabla}$,or left-differential operator,$overleftarrow{nabla}$. The direction of the arrow signifies the direction in which the operator acts, according to the book.
Does anybody have a clue on what do they mean with the "direction which the operator acts"?
[1] Capaldi, Franco. 2012. Continuum Mechanics : Constitutive Modeling of Structural and Biological Materials. Cambridge, MA: Cambridge University Press.
vector-analysis
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
$endgroup$
add a comment |
$begingroup$
Studying Continuum Mechanics with Capaldi's book [1, p.27], he states that
the gradient can each be expressed in terms of a vector differential operator named the Del operator, which is defined in Cartesian coordinates as either a right-differential operator, $overrightarrow{nabla}$,or left-differential operator,$overleftarrow{nabla}$. The direction of the arrow signifies the direction in which the operator acts, according to the book.
Does anybody have a clue on what do they mean with the "direction which the operator acts"?
[1] Capaldi, Franco. 2012. Continuum Mechanics : Constitutive Modeling of Structural and Biological Materials. Cambridge, MA: Cambridge University Press.
vector-analysis
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
$endgroup$
Studying Continuum Mechanics with Capaldi's book [1, p.27], he states that
the gradient can each be expressed in terms of a vector differential operator named the Del operator, which is defined in Cartesian coordinates as either a right-differential operator, $overrightarrow{nabla}$,or left-differential operator,$overleftarrow{nabla}$. The direction of the arrow signifies the direction in which the operator acts, according to the book.
Does anybody have a clue on what do they mean with the "direction which the operator acts"?
[1] Capaldi, Franco. 2012. Continuum Mechanics : Constitutive Modeling of Structural and Biological Materials. Cambridge, MA: Cambridge University Press.
vector-analysis
vector-analysis
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
asked Jan 11 at 17:09
Franks V. MaiaFranks V. Maia
132
132
add a comment |
add a comment |
1 Answer
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Normally an operator is placed to the left of what it's acting on: $nablaphi.$
But sometimes it is however useful to have it placed to the right of what it's acting on. Then an arrow is used to mark in what direction it acts: $phioverleftarrow{nabla}$.
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
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$begingroup$
Normally an operator is placed to the left of what it's acting on: $nablaphi.$
But sometimes it is however useful to have it placed to the right of what it's acting on. Then an arrow is used to mark in what direction it acts: $phioverleftarrow{nabla}$.
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
$endgroup$
add a comment |
$begingroup$
Normally an operator is placed to the left of what it's acting on: $nablaphi.$
But sometimes it is however useful to have it placed to the right of what it's acting on. Then an arrow is used to mark in what direction it acts: $phioverleftarrow{nabla}$.
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
$endgroup$
add a comment |
$begingroup$
Normally an operator is placed to the left of what it's acting on: $nablaphi.$
But sometimes it is however useful to have it placed to the right of what it's acting on. Then an arrow is used to mark in what direction it acts: $phioverleftarrow{nabla}$.
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
$endgroup$
Normally an operator is placed to the left of what it's acting on: $nablaphi.$
But sometimes it is however useful to have it placed to the right of what it's acting on. Then an arrow is used to mark in what direction it acts: $phioverleftarrow{nabla}$.
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
answered Jan 11 at 17:30
md2perpemd2perpe
7,96111028
7,96111028
add a comment |
add a comment |
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