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// Verify download URL. private URL verifyUrl(String url) { // Only allow HTTP URLs. if (!url.toLowerCase().startsWith("http://")) return null; // Verify format of URL. URL verifiedUrl = null; try { verifiedUrl = new URL(url); } catch (Exception e) { return null; } // Make sure URL specifies a file. if (verifiedUrl.getFile().length() < 2) return null; return verifiedUrl; }

Now, while a zero-sequence set of vectors is a balanced set (in accordance with the de nition following Fig. 259), note that the vector sum is NOT zero (as it is when the vectors are 1208 apart); instead, for a zero-sequence set we have that " " " " " " A0 B0 C0 3A0 3B0 3C0 452 " Thus, in the three equations that comprise eq. (450), we now add A0 to both sides of the " "0 to both sides of the second equation, and C0 to both sides of the third rst equation, B " " " equation. Then, letting A 0 A0 A, and so on, eq. (450) becomes 9 " " " " A1 A2 A0 A > = " " " " 453 B1 B2 B0 B > ; " " " " C1 C2 C0 C " " " where A, B, and C , without subscripts, represent three components of an equivalent unbalanced set of three vectors having the required six degrees of freedom. Thus we ve " " " now expressed an unbalanced set of vectors, A, B, C , in terms of the components of three balanced sets of vectors. Now suppose the components of an unbalanced set are known, and we wish to nd the values of the three equivalent balanced sets. That is, let the PROBLEM be: GIVEN the

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" " " values of an unbalanced set, A, B, and C , nd the values of the components of the three balanced sets whose vector sum is equal to the given unbalanced set. This would seem, o hand, to be a most di cult problem, but fortunately, because of the symmetry of balanced sets, it turns out not to be so hard after all. Let us proceed as follows. First, carefully note, again, the set of equations given just prior to eq. (450); doing this, and also keeping eq. (451) in mind, note that eq. (453) becomes (using degrees) " " " " A1 A2 A0 A " " " " A1 j120 A2 j240 A0 B " " " " A1 j240 A2 j120 A0 C Now, for convenience, let " a j120 then, also{ " a2 j240 and hence the foregoing three equations can be written in the easier-to-handle forms " " " " A1 A2 A0 A " " " " "" aA1 a2 A2 A0 B " " "" " " a2 A1 aA2 A0 C 455 456 457 454 *

This method first verifies that the URL entered is an HTTP URL since only HTTP is supported. Next, the URL being verified is used to construct a new URL class instance.

" " Note that we now have three simultaneous equations in three unknowns, A1 , A2 , and " A0 , the values of which can be found in several ways, including the method of elimination. Let us, however, use the more straightforward method of determinants, as follows. You ll recall that the rst step in the procedure is to nd the value of the determinant formed from the coe cients of the unknowns which, as you should now verify from inspection of the above three equations, is equal to 1 1 1 " " aa a D a a2 1 " "3 3" 2 2 a " " a 1 " " Or, since a j120 , then a3 j360 1, the above reduces to D 3" " 1 aa 458

To continue on, in our solution of eqs. (455) through (457), let us next nd the value of " A1 ; thus A 1 1 " " " B a2 1 C a 1 A "2 a B 1 a C 1 a2 " " "a " " " " " " A1 D 3" " 1 aa

If the URL is malformed, the URL class constructor will throw an exception. Finally, this method verifies that a file is actually specified in the URL.

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