http://editthis.info/VectorCalcUMB/?action=history&feed=atom&title=Hamiltonian_function 2026-10-13T22:27:06Z Revision history for this page on the wiki MediaWiki 1.15.1 http://editthis.info/VectorCalcUMB/?title=Hamiltonian_function&diff=1410&oldid=prev 2006-05-02T21:30:38Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 21:30, 2 May 2006</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 7:</td> <td colspan="2" class="diff-lineno">Line 7:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We call the total energy function the Hamiltonian Function, and denote it H. &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We call the total energy function the Hamiltonian Function, and denote it H. &nbsp;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">The paragraph: </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">For </ins>a <ins class="diffchange diffchange-inline">particle of mass m moving on a line</ins>. <ins class="diffchange diffchange-inline">Kinetic = p^2/2m</ins>. <ins class="diffchange diffchange-inline">If the particle </ins>is <ins class="diffchange diffchange-inline">moving under the influence of </ins>a <ins class="diffchange diffchange-inline">conservative force, </ins>like <ins class="diffchange diffchange-inline">gravity, then there is a potential energy, U, which is a function </ins>of <ins class="diffchange diffchange-inline">position</ins>.</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">&quot;But energy is more than just </del>a <del class="diffchange diffchange-inline">conserved quantity: it determines </del>..<del class="diffchange diffchange-inline">&quot; (pg.65) (1st page of Chpt 4) </del>is a <del class="diffchange diffchange-inline">dramatic pargraph and I </del>like <del class="diffchange diffchange-inline">it. We should start out with something </del>of <del class="diffchange diffchange-inline">this nature as an opening paragraph</del>. <del class="diffchange diffchange-inline">-aaron</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">H:=p^2/2m+U(r)</ins></div></td></tr> <!-- diff generator: internal 2026-10-13 22:27:06 --> </table>

Aaronwelles http://editthis.info/VectorCalcUMB/?title=Hamiltonian_function&diff=1406&oldid=prev 2006-05-02T20:56:15Z

<p></p> <p><b>New page</b></p><div>The total energy function. (pg. 65-66)<br /> <br /> In a closed physical system the energy of the system is constant as the system moves through time.<br /> <br /> Example: Ball being thrown into air: Total energy = p^2/2m +mgr (kinetic + potential)<br /> <br /> We call the total energy function the Hamiltonian Function, and denote it H. <br /> <br /> The paragraph: <br /> &quot;But energy is more than just a conserved quantity: it determines ..&quot; (pg.65) (1st page of Chpt 4) is a dramatic pargraph and I like it. We should start out with something of this nature as an opening paragraph. -aaron</div>

Aaronwelles