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2 canonical form.

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



Robert Corless
Wed Feb 4 14:46:04 EST 1998