Pendulum as a first-order system (Q1617): Difference between revisions
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| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: \\frac{d\\theta}{dt}=v,\\qquad \\frac{dv}{dt}=-\\frac{g}{L}\\sin\\theta,\\qquad \\text{equilibria at }(\\theta,v)=(0,0)\\ \\text{and}\\ (\\pi,0) / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
\\begin{cases}\n\\omega=\\frac{d\\theta}{dt} \\\\\n\\frac{d\\omega}{dt}=-\\frac{g}{L}\\sin\\theta\n\\end{cases} | |||
| Property / LaTeX source: \\begin{cases}\n\\omega=\\frac{d\\theta}{dt} \\\\\n\\frac{d\\omega}{dt}=-\\frac{g}{L}\\sin\\theta\n\\end{cases} / rank | |||
Normal rank | |||
| Property / note | |||
From equation 2 it can be inferred that equilibria is reached at $\\theta=0$ or $\\theta=\\pi$ | |||
| Property / note: From equation 2 it can be inferred that equilibria is reached at $\\theta=0$ or $\\theta=\\pi$ / rank | |||
Normal rank | |||
Latest revision as of 18:30, 10 October 2026
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pendulum as a first-order system |
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Statements
\\begin{cases}\n\\omega=\\frac{d\\theta}{dt} \\\\\n\\frac{d\\omega}{dt}=-\\frac{g}{L}\\sin\\theta\n\\end{cases}
0 references
From equation 2 it can be inferred that equilibria is reached at $\\theta=0$ or $\\theta=\\pi$
0 references