Consider a particle P of mass m moving freely in a Euclidean plane under the influence...

 

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Consider a particle P of mass m moving freely in a Euclidean plane under the influence of a constant force F. Introduce oblique Cartesian coordinates q¹, q² (x) = (² 9(²) x¹, x² being rectangular Cartesian. (a) Calculate the covariant basis vectors a¡ (i = 1,2) and the metric coefficients aap (a, ß = 1,2). (b) Write the position and velocity vectors of P using the covariant basis. (c) Apply Lagrange's equations in the form d at (300) - 30 = Qα = F·aa, (a = 1,2). dt əqa Consider a particle P of mass m moving freely in a Euclidean plane under the influence of a constant force F. Introduce oblique Cartesian coordinates q¹, q² (x) = (² 9(²) x¹, x² being rectangular Cartesian. (a) Calculate the covariant basis vectors a¡ (i = 1,2) and the metric coefficients aap (a, ß = 1,2). (b) Write the position and velocity vectors of P using the covariant basis. (c) Apply Lagrange's equations in the form d at (300) - 30 = Qα = F·aa, (a = 1,2). dt əqa

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Solutions Step 1 a We know that the covariant basis vectors are given by aixqi where x is the position vector of the particle in rectangular Cartesian ... View the full answer