14:06Done5In 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 = ¹½ m (x² + y² + 2²). To express the kinetic energy and potential energy insome other coordinate system requires a set of transformation equations.3.1Taking 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=2²² +mg | Cosи4G15un

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Consider a particle subject to the potential: V (x) : 1 + x² In other words: x' X' = y' dV dx x² -1 (x²+1)² Where: X(0) = C) ()- For what values of v does the particle reach x = 1?
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 + 2²). 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: 3.2 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 L = T-V = ²² +mg | Cos Write down the Lagrange equation for a single generalised coordinate q. State name the number of generalised coordinates in problem 3.1. Hence write…
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