- #1
Mind----Blown
- 11
- 0
Suppose i have an equilateral triangle and i want to find the principal axes of rotation passing through one of the vertex. How can i do that? I am thinking along the following lines but I'm not too sure:
1)Since the equilateral triangle has symmetry about a median, that definitely is one principal axis.
2)Now, i want 2 axes such that those 2 axes and the centroidal axis which i found above are mutually perpendicular. The problem now, however, is that i don't have any "symmetry" to rely on. Sure i COULD think along this line now :
"if i rotate the triangle 360 degrees about one of the sides, i would return to the original configuration, so let me choose that as one of the axis, which leaves me with only one choice for the third axis and voila!"
But i am not too sure of my approach in 2nd point since it just doesn't seem right; rotating an object 360 degrees to get the original configuration isn't really a symmetry!
1) So, is there some fool-proof way i can use (and be 100% certain of being correct) to determine principal axes of rotation?
2) Maybe mathematical?
3) Also, how reliable is this symmetry approach i follow?
1)Since the equilateral triangle has symmetry about a median, that definitely is one principal axis.
2)Now, i want 2 axes such that those 2 axes and the centroidal axis which i found above are mutually perpendicular. The problem now, however, is that i don't have any "symmetry" to rely on. Sure i COULD think along this line now :
"if i rotate the triangle 360 degrees about one of the sides, i would return to the original configuration, so let me choose that as one of the axis, which leaves me with only one choice for the third axis and voila!"
But i am not too sure of my approach in 2nd point since it just doesn't seem right; rotating an object 360 degrees to get the original configuration isn't really a symmetry!
1) So, is there some fool-proof way i can use (and be 100% certain of being correct) to determine principal axes of rotation?
2) Maybe mathematical?
3) Also, how reliable is this symmetry approach i follow?