Split data.frame row into multiple rows based on commas

I am attempting to split a row in a data.frame based on the character sequence ", ". Here's an example:

mydat <- data.frame(v1 = c("name, name2", "name3", "name4, name5"),
                v2 = c("1, 2", "3", "4, 5"), 
                v3 = c(1, 2, 3))

What I would like to end up with is a data.frame like so:

 v1   v2   v3
name  1    1
name2  2   1
name3  3   2
name4  4   2
name5  5   3

Any suggestions?