uni/mathmod/bonus2/e2.mw

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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plottools):</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_1_z := diff(z(t), t$2) = 1/m*(m*g - fA - fB - fC);</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_1_phi := diff(phi(t), t$2) = 1/I_r*(r*f-r*fB);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqb2RlXzFfcGhpRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYoLUkmbWZyYWNHRiQ2KC1JJW1zdXBHRiQ2JS1GNjYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZW4tSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRiM2JUZXLUZVNiUtRiw2JVEidEYnRi9GMkZnbkZbb0Y5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zqby8lKWJldmVsbGVkR0Y9LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjRlbUYnLyUmZGVwdGhHRmRwLyUqbGluZWJyZWFrR1ElYXV0b0YnLUYsNiVRJiZwaGk7RicvRjBGPUY5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZaRmZuLUkobWZlbmNlZEdGJDYkLUYjNiZGYm8vJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRj1GOUY5RjktRjY2LVEpJmVxdWFscztGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUZSNigtRiM2Ji1GIzYmLUYsNiVRInJGJ0YvRjItRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZaRmZuLUYsNiVRImZGJ0YvRjJGOS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmRzLUYjNiZGZ3JGanItRiw2JVEjZkJGJ0YvRjJGOUY5LUYsNiVRJElfckYnRi9GMkZlb0Zob0ZbcEZdcEY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpvZGVfMV9waGlHRigvLUklZGlmZkdGJjYkLUkkcGhpR0YoNiNJInRHRigtSSIkR0YmNiRGNSIiIyomSSRJX3JHRighIiIsJiomSSJmR0YoIiIiSSJyR0YoRkBGQComSSNmQkdGKEZARkFGQEY8RkA3Iy8tRjA2JC1GMDYkRjJGNUY1Rjo=</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L6" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">set_constraints := { z(t) = r/2*phi(t), phi(t) = -z(t)*2/r, fC = fB*exp(mu*Pi), fA = rho*g*A*z(t) };</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+STBzZXRfY29uc3RyYWludHNHRig8Ji9JI2ZBR0YoKipJJHJob0dGKCIiIkkiZ0dGKEYzSSJBR0YoRjMtSSJ6R0YoNiNJInRHRihGMy9JI2ZDR0YoKiZJI2ZCR0YoRjMtSSRleHBHRiU2IyomSSNtdUdGKEYzSSNQaUdGJkYzRjMvLUkkcGhpR0YoRjgsJComRjZGM0kickdGKCEiIiEiIy9GNiwkKiZGSUYzRkVGMyNGMyIiIzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L41" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_2_z := simplify(eval['recurse'](ode_1_z, set_constraints minus {set_constraints[4]}));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShvZGVfMl96R0YoLy1JJWRpZmZHRiY2JC1JInpHRig2I0kidEdGKC1JIiRHRiY2JEY1IiIjKiZJIm1HRighIiIsKiomRjsiIiJJImdHRihGP0Y/KipJJHJob0dGKEY/RkBGP0kiQUdGKEY/RjJGP0Y8SSNmQkdGKEY8KiZGREY/LUkkZXhwR0YlNiMqJkkjbXVHRihGP0kjUGlHRiZGP0Y/RjxGPzcjLy1GMDYkLUYwNiRGMkY1RjVGOg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L54" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_2_phi := diff(z(t), t$2) = solve((simplify(eval(ode_1_phi, set_constraints)), diff(z(t), t$2)));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpvZGVfMl9waGlHRigvLUklZGlmZkdGJjYkLUkiekdGKDYjSSJ0R0YoLUkiJEdGJjYkRjUiIiMsJCooSSJyR0YoRjksJkkiZkdGKCIiIkkjZkJHRighIiJGP0kkSV9yR0YoRkEjRkFGOTcjLy1GMDYkLUYwNiRGMkY1RjVGOg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L48" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_fB := fB = solve(eval(ode_2_z, {diff(z(t), t$2) = a}), fB);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZlcV9mQkdGKC9JI2ZCR0YoLCQqJiwoKipJJHJob0dGKCIiIkkiZ0dGKEY1SSJBR0YoRjUtSSJ6R0YoNiNJInRHRihGNUY1KiZJImFHRihGNUkibUdGKEY1RjUqJkY+RjVGNkY1ISIiRjUsJi1JJGV4cEdGJTYjKiZJI211R0YoRjVJI1BpR0YmRjVGNUY1RjVGQEZANyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L55" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_f := f(t) = solve(eval(ode_2_phi, {f = f(t), diff(z(t), t$2) = a}), f(t));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcV9mR0YoLy1JImZHRig2I0kidEdGKCwkKiYsJiomSSNmQkdGKCIiIkkickdGKCIiIyEiIiomSSRJX3JHRihGOEkiYUdGKEY4RjpGOEY5ISIjRjs3I0Yu</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_f_with_ics := simplify(eval(eval(eq_f, {eq_fB}), {z(t) = a/2*t^2}));</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS5lcV9mX3dpdGhfaWNzR0YoLy1JImZHRig2I0kidEdGKCwkKigsKCooSSJhR0YoIiIiSSRJX3JHRihGOC1JJGV4cEdGJTYjKiZJI211R0YoRjhJI1BpR0YmRjhGOCEiJSomLCYqJiwmKipJIkFHRihGOEkiZ0dGKEY4SSRyaG9HRihGOEYyIiIjISIiSSJtR0YoISIjRjhJInJHRihGSUY4RjlGQEY4RjdGOEY4KihGR0Y4RktGOEZNRklGSUY4LCZGOkY4RjhGOEZKRk1GTCNGOEZJNyNGLg==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">handschriftliche \303\234berpr\303\274fung:</Font></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(rhs(eq_f_with_ics) - (-2*I_r*a/r^2 + m/(1+exp(mu*Pi))*(g*(1-rho*A*a/(2*m)*t^2)-a)))</Text-field>
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<Group hide-input="false" labelreference="L58" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(rhs(eval(eq_f_with_ics, { g = 9.81, A = 10, r = 1, I_r = 4, m = 8, rho = 1, a = 0.1, mu = 0.9 })), t=0..100)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_f_spring := f = eval(k*2*z(t));</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_mu_zero := mu = 0;</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_3_z := eval(ode_2_z, {eq_f_spring, eq_mu_zero});</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShvZGVfM196R0YoLy1JJWRpZmZHRiY2JC1JInpHRig2I0kidEdGKC1JIiRHRiY2JEY1IiIjKiZJIm1HRighIiIsKComRjsiIiJJImdHRihGP0Y/KipJJHJob0dGKEY/RkBGP0kiQUdGKEY/RjJGP0Y8SSNmQkdGKCEiI0Y/NyMvLUYwNiQtRjA2JEYyRjVGNUY6</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L68" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_3_phi := eval(ode_2_phi, {eq_f_spring, eq_mu_zero});</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpvZGVfM19waGlHRigvLUklZGlmZkdGJjYkLUkiekdGKDYjSSJ0R0YoLUkiJEdGJjYkRjUiIiMsJCooSSJyR0YoRjksJiomSSJrR0YoIiIiRjJGQEY5SSNmQkdGKCEiIkZASSRJX3JHRihGQiNGQkY5NyMvLUYwNiQtRjA2JEYyRjVGNUY6</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L78" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_4_z := diff(z(t), t$2) = simplify(solve(simplify(eval(ode_3_z, {fB = solve(ode_3_phi, fB)})), diff(z(t), t$2)));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShvZGVfNF96R0YoLy1JJWRpZmZHRiY2JC1JInpHRig2I0kidEdGKC1JIiRHRiY2JEY1IiIjLCQqKEkickdGKEY5LCYqJiwmKihJIkFHRigiIiJJImdHRihGQkkkcmhvR0YoRkJGQkkia0dGKCIiJUZCRjJGQkZCKiZJIm1HRihGQkZDRkIhIiJGQiwmKiZGSEZCRjxGOUZCSSRJX3JHRihGRkZJRkk3Iy8tRjA2JC1GMDYkRjJGNUY1Rjo=</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L79" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ode_4_phi := diff(z(t), t$2) = simplify(solve(simplify(eval(ode_3_phi, {fB = solve(ode_3_z, fB)})), diff(z(t), t$2)));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqb2RlXzRfcGhpRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYoLUkmbWZyYWNHRiQ2KC1JJW1zdXBHRiQ2JS1GNjYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZW4tSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRiM2JUZXLUZVNiUtRiw2JVEidEYnRi9GMkZnbkZbb0Y5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zqby8lKWJldmVsbGVkR0Y9LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjRlbUYnLyUmZGVwdGhHRmRwLyUqbGluZWJyZWFrR1ElYXV0b0YnLUYsNiVRInpGJ0YvRjItRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRlpGZm4tSShtZmVuY2VkR0YkNiQtRiM2JkZiby8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5RjlGOS1GNjYtUSkmZXF1YWxzO0YnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiM2JS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZnItRlI2KC1GIzYmLUZVNiUtRiw2JVEickYnRi9GMkZnbkZbby1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRlpGZm4tRmRxNiQtRiM2Ji1GIzYmLUZkcTYkLUYjNiYtRiM2KC1GLDYlUSJBRidGL0YyRmFzLUYsNiVRImdGJ0YvRjJGYXMtRiw2JVEmJnJobztGJy9GMEY9RjlGOS1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkhGZXJGZ3ItRiM2Ji1GaG42JFEiNEYnRjlGYXMtRiw2JVEia0YnRi9GMkY5RjlGOUZhcy1GIzYmRl1xRmBxRmNxRjlGOS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRmVyRmdyLUYjNiYtRiw2JVEibUYnRi9GMkZhc0ZjdEY5RjlGOUY5LUYjNiYtRiM2JkZcdkZhc0Zcc0Y5Rmp0LUYjNiZGX3VGYXMtRiw2JVEkSV9yRidGL0YyRjlGOUZlb0Zob0ZbcEZdcEY5Rjk=">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpvZGVfNF9waGlHRigvLUklZGlmZkdGJjYkLUkiekdGKDYjSSJ0R0YoLUkiJEdGJjYkRjUiIiMsJCooSSJyR0YoRjksJiomLCYqKEkiQUdGKCIiIkkiZ0dGKEZCSSRyaG9HRihGQkZCSSJrR0YoIiIlRkJGMkZCRkIqJkkibUdGKEZCRkNGQiEiIkZCLCYqJkZIRkJGPEY5RkJJJElfckdGKEZGRklGSTcjLy1GMDYkLUYwNiRGMkY1RjVGOg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L86" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>