- #1

- 766

- 57

If i have a vector

**r**= ( x

_{1}, x

_{2}, x

_{3}) then i can write

**r**

^{2}as x

_{i}x

_{i}where the i is summed over because it occurs twice. Now is x

_{i}x

_{i}the same as x

_{i}

^{2}? I have come across an example where they are used as equivalent but i am confused because x

_{i}

^{2}seems to be the square of just one component of

**r**but x

_{i}

^{2}also seems to be logically the same as x

_{i}x

_{i}

My other question is ; are there some quantities that cannot be written in summation convention ? Such the kinetic energy of many particles . I have seen it written using sigma notation as the sum over k from 1 to N as m

_{k}

**v**but obviously k appears 3 times here. This applies to small oscillations where the

_{k}v_{k}**r**is differentiated with respect to different variables . Are some quantities impossible to write in summation convention ?

_{k}Thanks