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 + ²). 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 - i.e.angle between the string and the perpendicular is given by:L=T-V = 1²0² + mg | Cos 03.2Write down the Lagrange equation for a single generalised coordinate q.State name the number of generalised coordinates in problem 3.1.Hence write down the Lagrange equation of motion in terms of the identifiedgeneralised coordinates.

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3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length [, mass m, free to with angular displacement 8- i.e. angle between the string and the perpendicular is given by: L=T-V=²0² +mg | Cos

3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length [, mass m, free to with angular displacement 8- i.e. angle between the string and the perpendicular is given by: L=T-V=²0² +mg | Cos

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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 + ²). 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 - i.e.
angle between the string and the perpendicular is given by:
L=T-V = 1²0² + mg | Cos 0
3.2
Write down the Lagrange equation for a single generalised coordinate q.
State name the number of generalised coordinates in problem 3.1.
Hence write down the Lagrange equation of motion in terms of the identified
generalised coordinates.

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