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{
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"%plot --format svg"
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"setdefaults\n",
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"![square plate](./plate.png)\n",
"\n",
"Square plate 50 mm-by-50 mm is pinned at center of top and rotates with a torque, $\\tau(t)$=0.05 N-m. The plate has mass, m=0.8 kg. What is the rotation rate of the system and the resulting $\\theta(t)$? The plate starts at rest at 10$^{o}$ off the vertical position"
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"source": [
"function dy=myode(t,y,L,m,tau)\n",
" g=9.81;\n",
" dy=zeros(size(y));\n",
" dy(1)=12/m/L^2*tau-(6*y(1).*y(3).*sin(y(2)).*cos(y(2)))./(1+3*sin(y(2)).^2); % d/dt(dpsi/dt)=...\n",
" dy(2)=y(3); % d/dt(theta)=dtheta/dt\n",
" dy(3)=-12*g/L/2*sin(y(2))-3*y(1).^2.*sin(y(2)).*cos(y(2)); %d/dt(dtheta/dt)=...\n",
"end"
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"source": [
"[t,y]=ode23(@(t,y) myode(t,y,50e-3,0.8,0.05),[0,0.5],[0,pi/18,0]);"
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L426.8,214.9 L426.9,213.7 L427.0,212.4 L427.1,211.1 L427.2,209.8 L427.3,208.5 L427.4,207.1 L427.5,205.7 L427.6,204.2 L427.7,202.7 L427.8,201.1 L427.9,199.5 L428.0,197.8 L428.1,196.0 L428.2,194.1 L428.4,192.0 L428.5,189.7 L428.7,187.3 L428.9,184.9 L429.0,182.5 L429.2,180.1 L429.3,178.0 L429.4,176.1 L429.6,174.3 L429.7,172.7 L429.8,171.1 L429.9,169.7 L430.0,168.2 L430.1,166.8 L430.2,165.5 L430.3,164.2 L430.4,162.9 L430.4,161.7 L430.5,160.5 L430.6,159.4 L430.7,158.2 L430.8,157.1 L430.9,156.0 L430.9,155.0 L431.0,154.0 L431.1,153.0 L431.2,152.0 L431.2,151.0 L431.3,150.1 L431.4,149.2 L431.5,148.3 L431.5,147.4 L431.6,146.6 L431.7,145.7 L431.8,144.9 L431.8,144.1 L431.9,143.4 L432.0,142.6 L432.0,141.9 L432.1,141.1 L432.2,140.4 L432.2,139.7 L432.3,139.1 L432.4,138.4 L432.4,137.8 L432.5,137.1 L432.6,136.5 L432.6,135.9 L432.7,135.4 L432.7,134.8 L432.8,134.3 L432.9,133.7 L432.9,133.2 L433.0,132.7 L433.0,132.2 L433.1,131.7 L433.2,131.3 L433.2,130.8 L433.3,130.4 L433.3,130.0 L433.4,129.5 L433.4,129.2 L433.5,128.8 L433.5,128.4 L433.6,128.0 L433.6,127.7 L433.7,127.3 L433.8,127.0 L433.8,126.7 L433.9,126.4 L433.9,126.1 L434.0,125.8 L434.0,125.6 L434.1,125.3 L434.1,125.0 L434.2,124.8 L434.2,124.6 L434.2,124.3 L434.3,124.1 L434.3,123.9 L434.4,123.7 L434.4,123.5 L434.5,123.4 L434.5,123.2 L434.6,123.0 L434.6,122.9 L434.6,122.7 L434.7,122.6 L434.7,122.5 L434.8,122.4 L434.8,122.2 L434.9,122.1 L434.9,122.0 L434.9,121.9 L435.0,121.8 L435.0,121.7 L435.1,121.6 L435.1,121.5 L435.2,121.4 L435.2,121.3 L435.3,121.3 L435.3,121.2 L435.4,121.2 L435.4,121.1 L435.5,121.1 L435.6,121.1 L435.6,121.0 L435.7,121.0 L435.8,121.1 L435.9,121.1 L435.9,121.2 L436.0,121.2 L436.0,121.3 L436.1,121.3 L436.1,121.4 L436.2,121.5 L436.2,121.6 L436.3,121.7 L436.3,121.8 L436.4,121.9 L436.4,122.0 L436.4,122.1 L436.5,122.2 L436.5,122.3 L436.6,122.4 L436.6,122.5 L436.6,122.6 L436.7,122.7 L436.7,122.9 L436.8,123.0 L436.8,123.2 L436.8,123.3 L436.9,123.5 L436.9,123.7 L437.0,123.9 L437.0,124.1 L437.1,124.3 L437.1,124.5 L437.1,124.7 L437.2,124.9 L437.2,125.1 L437.3,125.4 L437.3,125.7 L437.4,125.9 L437.4,126.2 L437.5,126.5 L437.5,126.8 L437.6,127.1 L437.6,127.4 L437.7,127.7 L437.7,128.1 L437.8,128.4 L437.8,128.8 L437.9,129.1 L437.9,129.5 L438.0,129.9 L438.0,130.3 L438.1,130.7 L438.1,131.2 L438.2,131.6 L438.3,132.1 L438.3,132.6 L438.4,133.0 L438.4,133.5 L438.5,134.0 L438.5,134.6 L438.6,135.1 L438.7,135.6 L438.7,136.2 L438.8,136.8 L438.8,137.4 L438.9,138.0 L439.0,138.6 L439.0,139.2 L439.1,139.9 L439.1,140.5 L439.2,141.2 L439.3,141.9 L439.3,142.6 L439.4,143.3 L439.5,144.1 L439.5,144.8 L439.6,145.6 L439.7,146.4 L439.7,147.2 L439.8,148.0 L439.9,148.9 L439.9,149.7 L440.0,150.6 L440.1,151.5 L440.2,152.4 L440.2,153.4 L440.3,154.3 L440.4,155.3 L440.4,156.3 L440.5,157.3 L440.6,158.3 L440.7,159.4 L440.8,160.5 L440.8,161.6 L440.9,162.7 L441.0,163.9 L441.1,165.0 L441.2,166.2 L441.2,167.5 L441.3,168.7 L441.4,170.0 L441.5,171.4 L441.6,172.7 L441.7,174.2 L441.8,175.6 L441.9,177.1 L442.0,178.7 L442.1,180.3 L442.2,182.0 L442.3,183.8 L442.5,185.7 L442.6,187.8 L442.7,190.2 L442.9,192.6 L443.1,195.0 L443.2,197.4 L443.4,199.6 L443.5,201.6 L443.6,203.4 L443.7,205.1 L443.8,206.6 L443.9,208.2 L444.0,209.6 L444.1,211.0 L444.2,212.3 L444.3,213.6 L444.4,214.9 L444.5,216.1 L444.6,217.3 L444.6,218.5 L444.7,219.6 L444.8,220.7 L444.9,221.8 L445.0,222.8 L445.0,223.8 L445.1,224.8 L445.2,225.8 L445.3,226.8 L445.3,227.7 L445.4,228.6 L445.5,229.5 L445.5,230.4 L445.6,231.2 L445.7,232.1 L445.8,232.9 L445.8,233.7 L445.9,234.4 L446.0,235.2 L446.0,235.9 L446.1,236.6 L446.2,237.4 L446.2,238.0 L446.3,238.7 L446.3,239.4 L446.4,240.0 L446.5,240.6 L446.5,241.2 L446.6,241.8 L446.6,242.4 L446.7,243.0 L446.8,243.5 L446.8,244.0 L446.9,244.6 L446.9,245.1 L447.0,245.6 L447.1,246.0 L447.1,246.5 L447.2,247.0 L447.2,247.4 L447.3,247.8 L447.3,248.2 L447.4,248.6 L447.4,249.0 L447.5,249.4 L447.5,249.8 L447.6,250.1 L447.6,250.4 L447.7,250.8 L447.7,251.1 L447.8,251.4 L447.8,251.7 L447.9,252.0 L447.9,252.2 L448.0,252.5 L448.0,252.8 L448.1,253.0 L448.1,253.2 L448.2,253.5 L448.2,253.7 L448.3,253.9 L448.3,254.1 L448.4,254.3 L448.4,254.4 L448.4,254.6 L448.5,254.8 L448.5,254.9 L448.6,255.1 L448.6,255.2 L448.6,255.4 L448.7,255.5 L448.7,255.6 L448.8,255.7 L448.8,255.8 L448.8,255.9 L448.9,256.0 L448.9,256.1 L448.9,256.2 L449.0,256.2 L449.0,256.3 L449.0,256.4 L449.1,256.4 L449.1,256.5 L449.2,256.6 L449.2,256.7 L449.3,256.7 L449.3,256.8 L449.4,256.8 L449.5,256.8 L449.5,256.9 L449.6,256.9 L449.7,256.8 L449.8,256.8 L449.8,256.7 L449.9,256.7 L449.9,256.6 L450.0,256.6 L450.0,256.5 L450.1,256.4 L450.1,256.3 L450.2,256.2 L450.2,256.1 L450.3,256.0 L450.3,255.9 L450.3,255.8 L450.4,255.7 L450.4,255.6 L450.4,255.5 L450.5,255.4 L450.5,255.3 L450.5,255.2 L450.6,255.0 L450.6,254.9 L450.7,254.7 L450.7,254.6 L450.7,254.4 L450.8,254.2 L450.8,254.1 L450.9,253.9 L450.9,253.7 L451.0,253.5 L451.0,253.2 L451.0,253.0 L451.1,252.8 L451.1,252.5 L451.2,252.3 L451.2,252.0 L451.3,251.8 L451.3,251.5 L451.4,251.2 L451.4,250.9 L451.5,250.6 L451.5,250.2 L451.6,249.9 L451.6,249.6 L451.7,249.2 L451.7,248.8 L451.8,248.5 L451.8,248.1 L451.9,247.7 L451.9,247.3 L452.0,246.8 L452.0,246.4 L452.1,245.9 L452.1,245.5 L452.2,245.0 L452.2,244.5 L452.3,244.0 L452.4,243.5 L452.4,243.0 L452.5,242.4 L452.5,241.9 L452.6,241.3 L452.6,240.7 L452.7,240.1 L452.8,239.5 L452.8,238.9 L452.9,238.3 L452.9,237.6 L453.0,236.9 L453.1,236.3 L453.1,235.6 L453.2,234.8 L453.2,234.1 L453.3,233.4 L453.4,232.6 L453.4,231.8 L453.5,231.0 L453.6,230.2 L453.6,229.4 L453.7,228.5 L453.8,227.7 L453.8,226.8 L453.9,225.9 L454.0,225.0 L454.1,224.0 L454.1,223.1 L454.2,222.1 L454.3,221.1 L454.3,220.0 L454.4,219.0 L454.5,217.9 L454.6,216.8 L454.6,215.7 L454.7,214.6 L454.8,213.4 L454.9,212.2 L455.0,211.0 L455.1,209.8 L455.1,208.5 L455.2,207.2 L455.3,205.8 L455.4,204.4 L455.5,203.0 L455.6,201.5 L455.7,199.9 L455.8,198.3 L455.9,196.6 L456.0,194.8 L456.1,192.9 L456.3,190.8 L456.4,188.4 L456.6,186.0 L456.7,183.7 L456.9,181.3 L457.0,179.2 L457.1,177.3 L457.3,175.6 L457.4,173.9 L457.5,172.4 L457.6,170.9 L457.7,169.5 L457.8,168.2 L457.8,166.9 L457.9,165.6 L458.0,164.4 L458.1,163.2 L458.2,162.0 L458.3,160.9 L458.3,159.8 L458.4,158.7 L458.5,157.6 L458.6,156.6 L458.6,155.6 L458.7,154.6 L458.8,153.7 L458.9,152.7 L458.9,151.8 L459.0,150.9 L459.1,150.1 L459.1,149.2 L459.2,148.4 L459.3,147.6 L459.3,146.8 L459.4,146.0 L459.5,145.2 L459.5,144.5 L459.6,143.8 L459.7,143.1 L459.7,142.4 L459.8,141.7 L459.8,141.1 L459.9,140.4 L460.0,139.8 L460.0,139.2 L460.1,138.6 L460.1,138.0 L460.2,137.4 L460.2,136.9 L460.3,136.4 L460.4,135.8 L460.4,135.3 L460.5,134.8 L460.5,134.4 L460.6,133.9 L460.6,133.4 L460.7,133.0 L460.7,132.6 L460.8,132.2 L460.8,131.8 L460.9,131.4 L461.0,131.0 L461.0,130.6 L461.1,130.3 L461.1,129.9 L461.2,129.6 L461.2,129.3 L461.2,129.0 L461.3,128.7 L461.3,128.4 L461.4,128.1 L461.4,127.8 L461.5,127.6 L461.5,127.3 L461.6,127.1 L461.6,126.9 L461.7,126.6 L461.7,126.4 L461.7,126.2 L461.8,126.0 L461.8,125.9 L461.9,125.7 L461.9,125.5 L462.0,125.4 L462.0,125.2 L462.0,125.1 L462.1,124.9 L462.1,124.8 L462.2,124.7 L462.2,124.6 L462.2,124.5 L462.3,124.4 L462.3,124.3 L462.3,124.2 L462.4,124.1 L462.4,124.0 L462.4,123.9 L462.5,123.9 L462.5,123.8 L462.6,123.7 L462.6,123.6 L462.7,123.5 L462.8,123.5 L462.8,123.4 L462.9,123.4 L463.0,123.4 L463.0,123.3 L463.0,123.4 L463.1,123.4 L463.2,123.4 L463.2,123.5 L463.3,123.5 L463.3,123.6 L463.4,123.6 L463.4,123.7 L463.5,123.7 L463.5,123.8 L463.5,123.9 L463.6,124.0 L463.6,124.1 L463.7,124.2 L463.7,124.3 L463.7,124.4 L463.8,124.4 L463.8,124.6 L463.8,124.7 L463.9,124.8 L463.9,124.9 L463.9,125.0 L464.0,125.2 L464.0,125.3 L464.1,125.4 L464.1,125.6 L464.1,125.8 L464.2,125.9 L464.2,126.1 L464.3,126.3 L464.3,126.5 L464.3,126.7 L464.4,126.9 L464.4,127.1 L464.5,127.4 L464.5,127.6 L464.6,127.9 L464.6,128.1 L464.7,128.4 L464.7,128.7 L464.7,128.9 L464.8,129.2 L464.8,129.5 L464.9,129.9 L464.9,130.2 L465.0,130.5 L465.0,130.9 L465.1,131.2 L465.1,131.6 L465.2,132.0 L465.2,132.4 L465.3,132.8 L465.3,133.2 L465.4,133.7 L465.4,134.1 L465.5,134.5 L465.5,135.0 L465.6,135.5 L465.6,136.0 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L471.9,225.0 L472.0,225.9 L472.1,226.8 L472.1,227.7 L472.2,228.5 L472.3,229.4 L472.3,230.2 L472.4,231.0 L472.5,231.7 L472.5,232.5 L472.6,233.3 L472.6,234.0 L472.7,234.7 L472.8,235.4 L472.8,236.1 L472.9,236.7 L472.9,237.4 L473.0,238.0 L473.1,238.6 L473.1,239.2 L473.2,239.8 L473.2,240.4 L473.3,240.9 L473.3,241.4 L473.4,242.0 L473.5,242.5 L473.5,243.0 L473.6,243.5 L473.6,243.9 L473.7,244.4 L473.7,244.8 L473.8,245.3 L473.8,245.7 L473.9,246.1 L473.9,246.5 L474.0,246.9 L474.0,247.2 L474.1,247.6 L474.1,247.9 L474.2,248.3 L474.2,248.6 L474.3,248.9 L474.3,249.2 L474.4,249.5 L474.4,249.8 L474.4,250.1 L474.5,250.3 L474.5,250.6 L474.6,250.8 L474.6,251.1 L474.7,251.3 L474.7,251.5 L474.8,251.7 L474.8,251.9 L474.8,252.1 L474.9,252.3 L474.9,252.4 L475.0,252.6 L475.0,252.8 L475.0,252.9 L475.1,253.0 L475.1,253.2 L475.1,253.3 L475.2,253.4 L475.2,253.5 L475.3,253.6 L475.3,253.7 L475.3,253.8 L475.4,253.9 L475.4,254.0 L475.4,254.1 L475.5,254.1 L475.5,254.2 L475.5,254.3 L475.6,254.3 L475.6,254.4 L475.6,254.5 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L498.7,242.8 L498.7,243.2 L498.8,243.7 L498.8,244.1 L498.9,244.5 L498.9,244.9 L499.0,245.2 L499.0,245.6 L499.1,245.9 L499.1,246.3 L499.1,246.6 L499.2,246.9 L499.2,247.2 L499.3,247.5 L499.3,247.8 L499.4,248.1 L499.4,248.3 L499.5,248.6 L499.5,248.8 L499.5,249.1 L499.6,249.3 L499.6,249.5 L499.7,249.7 L499.7,249.9 L499.7,250.1 L499.8,250.3 L499.8,250.5 L499.9,250.7 L499.9,250.8 L499.9,251.0 L500.0,251.1 L500.0,251.2 L500.0,251.4 L500.1,251.5 L500.1,251.6 L500.1,251.7 L500.2,251.8 L500.2,251.9 L500.2,252.0 L500.3,252.1 L500.3,252.2 L500.3,252.3 L500.4,252.3 L500.4,252.4 L500.5,252.5 L500.5,252.6 L500.6,252.7 L500.6,252.8 L500.7,252.8 L500.8,252.9 L500.9,252.9 L501.0,252.9 L501.0,252.8 L501.1,252.8 L501.2,252.7 L501.2,252.6 L501.3,252.6 L501.3,252.5 L501.4,252.4 L501.4,252.3 L501.5,252.2 L501.5,252.1 L501.5,252.0 L501.6,251.9 L501.6,251.8 L501.6,251.7 L501.7,251.6 L501.7,251.5 L501.7,251.4 L501.8,251.2 L501.8,251.1 L501.8,251.0 L501.9,250.8 L501.9,250.7 L501.9,250.5 L502.0,250.3 L502.0,250.2 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"source": [
"plot(t,y(:,2)*180/pi)\n",
"xlabel('time (s)')\n",
"ylabel('theta (deg)')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
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},
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