# (Central Force and Euler-Lagrange equation) Given a system of m mass .docx

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(Central Force and Euler-Lagrange equation) Given a system of m mass particles that move with the influence of the central force which is screened. e(-r/a) V(r) where a is a constant that is always negative and a is a constant that is always positive andr is the radical distance between particles and potential sources. Write the Lagrangian of this system in the polar coordinate system and sketch the effective . 1) potential form (Veff) of the system for the case From this form of effective potential, what shape the trajectory might be experienced by the particle and also determine the energy that must be possessed by the particle to obtain the possible trajectory of the motion. Is there a stable path? Determine the radius of the orbit (radial distance) to obtain this stable path (if any) b. Write the Lagrangian of this system in the polar coordinate system and sketch the effective (1) From this form of effective potential form (Veff) of the system for the case
• Fall '19
• Force, Coordinate system, Polar coordinate system, Noether's theorem, potential sources, Central Force

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