In Lagrangian mechanics, the Lagrangian technique tells us that when dealing withparticles or rigid bodies that can be treated as particles, the Lagrangian can be definedas:L = T-V where T is the kinetic energy of the particle, and V the potential energy of theparticle. It is also advised to start with Cartesian coordinates when expressing thekinetic energy and potential energy components of the Lagrangiane.g. T = m (x² + y² + ż²). To express the kinetic energy and potential energy insome other coordinate system requires a set of transformation equations.3.1 Taking into consideration the information given above, show that the Lagrangianfor a pendulum of length 1, mass m, free to with angular displacement 0- i.e.angle between the string and the perpendicular is given by:L=T-V=1²0² + mg | Cos

Say we have a pendulum of mass m, length l which makes an angular displacement θ with the vertical.…

3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement 0- i.e. angle between the string and the perpendicular is given by: L=T-V = 1²0² +mg | Cos

3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement 0- i.e. angle between the string and the perpendicular is given by: L=T-V = 1²0² +mg | Cos

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.36P

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Question

In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with
particles or rigid bodies that can be treated as particles, the Lagrangian can be defined
as:
L = T-V where T is the kinetic energy of the particle, and V the potential energy of the
particle. It is also advised to start with Cartesian coordinates when expressing the
kinetic energy and potential energy components of the Lagrangian
e.g. T = m (x² + y² + ż²). To express the kinetic energy and potential energy in
some other coordinate system requires a set of transformation equations.
3.1 Taking into consideration the information given above, show that the Lagrangian
for a pendulum of length 1, mass m, free to with angular displacement 0- i.e.
angle between the string and the perpendicular is given by:
L=T-V=1²0² + mg | Cos

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