M3 Statics of Rigid Bodies

http://imgur.com/5HFDME5
Can someone explain the part in the red outline? Why are some of the terms ignored? Also if dr goes to 0, doesnt the whole thing just become 0?

Reply 1

atsruser

Original post by utah

http://imgur.com/5HFDME5
Can someone explain the part in the red outline? Why are some of the terms ignored? Also if dr goes to 0, doesnt the whole thing just become 0?

The explanation is poor. They are trying to say this (I've left out constants for ease of latexing):

r^3 \delta r + r^2 (\delta r)^2 + r(\delta r)^3 + (\delta r)^4 = (r^2 \delta r + r(\delta r)^2 + (\delta r)^3)\bar{y}

Now divide both sides by

\delta r

which is OK, since it's non-zero, and we get:

r^3 + r^2 \delta r + r(\delta r)^2 + (\delta r)^3 = (r^2 + r(\delta r) + (\delta r)^2)\bar{y}

Now let

\delta r \to 0

and all terms except the first on each side become arbitrarily small. That is why they can ignore some terms straight off - because in the final step, they will go to 0 anyway.