Consider a point particle of mass m moving in one dimension with potential V(x). The system is governed by the Lagrangian, L = 2m²i¹ +m³²V - XV² where is a constant parameter. Show that can be adjusted so that the resulting equation of motion is equivalent to the one that arises from the more familiar L = m² - V.
Consider a point particle of mass m moving in one dimension with potential V(x). The system is governed by the Lagrangian, L = 2m²i¹ +m³²V - XV² where is a constant parameter. Show that can be adjusted so that the resulting equation of motion is equivalent to the one that arises from the more familiar L = m² - V.
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Transcribed Image Text:Consider a point particle of mass m moving in one dimension with potential V(x). The system is
governed by the Lagrangian,
L = m²i^² + m²V - XV²
where > is a constant parameter. Show that can be adjusted so that the resulting equation of
motion is equivalent to the one that arises from the more familiar L = m² - V.
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