Mixing
How to apply d/dt to solve for equations of motion (Applying Lagrangian to Vibrations)
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In my engineering vibrations course, I am encountering derivatives that are partial as well as total. I am a little rusty and am having a really hard time grasping why the differentiation with respect to time is done differently in some scenarios.
Here is an example from my book:
I circled the two confusing terms in red and green. Why is the red term using chain rule while the green term simply takes a derivative with respect to x_dot?
derivatives euler-lagrange-equation
asked Jan 29 at 3:23
LearnITLearnIT
355
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add a comment |
$begingroup$
In my engineering vibrations course, I am encountering derivatives that are partial as well as total. I am a little rusty and am having a really hard time grasping why the differentiation with respect to time is done differently in some scenarios.
Here is an example from my book:
I circled the two confusing terms in red and green. Why is the red term using chain rule while the green term simply takes a derivative with respect to x_dot?
derivatives euler-lagrange-equation
asked Jan 29 at 3:23
LearnITLearnIT
355
$endgroup$
add a comment |
$begingroup$
In my engineering vibrations course, I am encountering derivatives that are partial as well as total. I am a little rusty and am having a really hard time grasping why the differentiation with respect to time is done differently in some scenarios.
Here is an example from my book:
I circled the two confusing terms in red and green. Why is the red term using chain rule while the green term simply takes a derivative with respect to x_dot?
derivatives euler-lagrange-equation
asked Jan 29 at 3:23
LearnITLearnIT
355
$endgroup$
In my engineering vibrations course, I am encountering derivatives that are partial as well as total. I am a little rusty and am having a really hard time grasping why the differentiation with respect to time is done differently in some scenarios.
Here is an example from my book:
I circled the two confusing terms in red and green. Why is the red term using chain rule while the green term simply takes a derivative with respect to x_dot?
derivatives euler-lagrange-equation
derivatives euler-lagrange-equation
asked Jan 29 at 3:23
LearnITLearnIT
355
asked Jan 29 at 3:23
LearnITLearnIT
355
asked Jan 29 at 3:23
LearnITLearnIT
355
asked Jan 29 at 3:23
LearnITLearnIT
355
asked Jan 29 at 3:23
LearnITLearnIT
355
355
add a comment |
add a comment |
1 Answer
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It is
$$ddot{x}/dt=ddot{x}$$
but
$$d(dot{x}^2)/dt=2dot{x},ddot{x}/dt=2dot{x}ddot{x}$$
answered Jan 29 at 5:41
MASLMASL
708313
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
It is
$$ddot{x}/dt=ddot{x}$$
but
$$d(dot{x}^2)/dt=2dot{x},ddot{x}/dt=2dot{x}ddot{x}$$
answered Jan 29 at 5:41
MASLMASL
708313
$endgroup$
add a comment |
$begingroup$
It is
$$ddot{x}/dt=ddot{x}$$
but
$$d(dot{x}^2)/dt=2dot{x},ddot{x}/dt=2dot{x}ddot{x}$$
answered Jan 29 at 5:41
MASLMASL
708313
$endgroup$
add a comment |
$begingroup$
It is
$$ddot{x}/dt=ddot{x}$$
but
$$d(dot{x}^2)/dt=2dot{x},ddot{x}/dt=2dot{x}ddot{x}$$
answered Jan 29 at 5:41
MASLMASL
708313
$endgroup$
It is
$$ddot{x}/dt=ddot{x}$$
but
$$d(dot{x}^2)/dt=2dot{x},ddot{x}/dt=2dot{x}ddot{x}$$
answered Jan 29 at 5:41
MASLMASL
708313
answered Jan 29 at 5:41
MASLMASL
708313
answered Jan 29 at 5:41
MASLMASL
708313
answered Jan 29 at 5:41
MASLMASL
708313
708313
add a comment |
add a comment |
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