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
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 + 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18074b88-9afc-40ca-8114-96bdef978bcb%2F9341078d-b752-455a-a4c3-c6bd4f2722a3%2Fqu7ykr9_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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