Comment on I'm too stupid for this
bitwolf@sh.itjust.works 4 days agoSo… Like to find the optimal impact angle to send an object towards a target?
The largest eigenvector would be the most probable direction of the struck object after impact?
Comment on I'm too stupid for this
bitwolf@sh.itjust.works 4 days agoSo… Like to find the optimal impact angle to send an object towards a target?
The largest eigenvector would be the most probable direction of the struck object after impact?
WolfLink@sh.itjust.works 4 days ago
Usually it is something like the eigenvectors represent stable states of the system, and other states will tend to be unstable until and end up in one of those stable states.
For example, the eigenvectors of the moment of inertia tensor represent “principle axes” of rotation, and these represent the possible stable axes of rotation (usually only one or two axes is actually stable, it depends on the object).
By analyzing principle axes of inertia, you can explain why a frisbee’s rotation is very stable around one axis but unstable around all other axes. And you can predict this kind of behavior for other objects.
Another example is in quantum mechanics, eigenvectors correspond to states that result after “measurement collapse” of the wavefunction, and are useful in various quantum mechanics problems, such as predicting the behavior of atoms, molecules, or semiconductors.