Based on the positions of these springs, how are we able to tell that this is a spiraling in pattern? I can see that two of the springs are contracting, one is neither stretched nor compressed, and the other is stretched. Is there anything else about the springs, like the magnitude of the compression, or its position, that can help us infer what the aggregate end result would be?
moridin22
If you remember some things from physics, one way of looking at phase space is that the squared norm of a vector from the origin to a particular point is related to the energy of the system at that point, since energy is given by kinetic+potential = 1/2mv^2 + 1/2kx^2, and the squared norm is x^2+v^2. Without any damping, the energy of the system stays the same, which is why we have circles. Then when we add damping, the energy of the system reduces over time, so the norm of the vector shrinks and thus we get spiraling in towards the origin.
Based on the positions of these springs, how are we able to tell that this is a spiraling in pattern? I can see that two of the springs are contracting, one is neither stretched nor compressed, and the other is stretched. Is there anything else about the springs, like the magnitude of the compression, or its position, that can help us infer what the aggregate end result would be?
If you remember some things from physics, one way of looking at phase space is that the squared norm of a vector from the origin to a particular point is related to the energy of the system at that point, since energy is given by kinetic+potential = 1/2mv^2 + 1/2kx^2, and the squared norm is x^2+v^2. Without any damping, the energy of the system stays the same, which is why we have circles. Then when we add damping, the energy of the system reduces over time, so the norm of the vector shrinks and thus we get spiraling in towards the origin.