The form is equivalent to , under , . This 2 form is very useful. For example,

But or d'Alembert. So if we try to choose , in general so that , instead of forcing , we will get this second form. Therefore

But these are the same equation! Assuming for the moment that , where is one of or , we have

Along = constant, we have (because ) so we have

defines
two integral curves,
which give us our ,

*Example*

Hence , **B = 0**, . This gives

or and

when const when
const

Put and , then (!).
Pictures are radial lines and
hyperbolae. Notice that they are tangential, ie. nontransversal, at
**x = 0** or **y =
0**

**Exercise:**

Show , , , ,
, , and hence

Wed Feb 4 14:46:04 EST 1998