Intuitively, what does it mean with respect to the motion to have spatial derivatives?
Lyynnn
Do you mean dq/dt? You can think of it as (q2 - q1)/(t2 - t1) and t2-t1 is very small. So the numerator denotes the position change, and the denominator is time change. (q2 - q1)/(t2 - t1) means distance/time which is the speed.
kencheng
Just to double-check here, q_dot is dq/dt, right? It's weird to see them both appear in the same equation if they were the same thing.
tulum
@sushain We can think about the temperature, it is a function of both the
spatial variable x, giving the position along the rod, and of the time t. --Brad Osgood The keyword is the Heat Equation:
ecohen2
@kencheng that was my understanding as well! but he also said in lecture "... with regards to time including d/dq and q dot" so I am also a little bit confused
Intuitively, what does it mean with respect to the motion to have spatial derivatives?
Do you mean dq/dt? You can think of it as (q2 - q1)/(t2 - t1) and t2-t1 is very small. So the numerator denotes the position change, and the denominator is time change. (q2 - q1)/(t2 - t1) means distance/time which is the speed.
Just to double-check here, q_dot is dq/dt, right? It's weird to see them both appear in the same equation if they were the same thing.
@sushain We can think about the temperature, it is a function of both the spatial variable x, giving the position along the rod, and of the time t. --Brad Osgood
The keyword is the Heat Equation:
@kencheng that was my understanding as well! but he also said in lecture "... with regards to time including d/dq and q dot" so I am also a little bit confused