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A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for describing a double pendulum free to move in a plane in gravity g? Assume the connecting rods are rigid. 141 m₂ L2 m₂2 Hint: Let's just assume L₁ = L₂ = 1 and that m₁ = m₂ = m and show that the Lagrangian reduces to : 2 2 L = {m²² (0₂² +40₁² +3010₂ cos(01 − 0₂)) + ½mgl (3 cos 0₁ + cos 0₂).

A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for describing a double pendulum free to move in a plane in gravity g? Assume the connecting rods are rigid. 141 m₂ L2 m₂2 Hint: Let's just assume L₁ = L₂ = 1 and that m₁ = m₂ = m and show that the Lagrangian reduces to : 2 2 L = {m²² (0₂² +40₁² +3010₂ cos(01 − 0₂)) + ½mgl (3 cos 0₁ + cos 0₂).

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A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for describing a double pendulum free to move in a plane in gravity g? Assume the connecting rods are rigid. 4₁ m₁ L₂ m₂²₂ Hint: Let's just assume L₁ 2 2 L = ¼m²³² (0₂² +401² +30₁02 cos(0₁ - 0₂)) + ½ mgl (3 cos 0₁ + cos 0₂). L₂ = 1 and that m₁ = m₂ = m and show that the Lagrangian reduces to :
Transcribed Image Text:A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for describing a double pendulum free to move in a plane in gravity g? Assume the connecting rods are rigid. 4₁ m₁ L₂ m₂²₂ Hint: Let's just assume L₁ 2 2 L = ¼m²³² (0₂² +401² +30₁02 cos(0₁ - 0₂)) + ½ mgl (3 cos 0₁ + cos 0₂). L₂ = 1 and that m₁ = m₂ = m and show that the Lagrangian reduces to :
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