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Consider a particle of mass m moving in 3-dimensions in a force field of the form (as expressed in Cartesian coordinates): Ix + yỹ + zà (z² + y? + 2?)/ F(z,y, 2) = K- where K is a constant. 1. Write down the Lagrangian and Lagrange's equations of motion for this particle in Cartesian coordinates - L(z, y, 2, ż, j, ż) 2. Now, transform the coordinate system to cylindrical coordinates: I = pcos o y = p sin o so that you can write the Lagrangian and Lagrange's equations of motion for the particle in cylindrical coordinates - L(p, 0, z, p, 0, ż).

Consider a particle of mass m moving in 3-dimensions in a force field of the form (as expressed in Cartesian coordinates): Ix + yỹ + zà (z² + y? + 2?)/ F(z,y, 2) = K- where K is a constant. 1. Write down the Lagrangian and Lagrange's equations of motion for this particle in Cartesian coordinates - L(z, y, 2, ż, j, ż) 2. Now, transform the coordinate system to cylindrical coordinates: I = pcos o y = p sin o so that you can write the Lagrangian and Lagrange's equations of motion for the particle in cylindrical coordinates - L(p, 0, z, p, 0, ż).

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Consider a particle of mass m moving in 3-dimensions in a force field of the form (as expressed in Cartesian coordinates): IX + vỹ + zż F(z, y, z) = K- (z2 + y? + z?)3/2' where K is a constant. 1. Write down the Lagrangian and Lagrange's equations of motion for this particle in Cartesian coordinates - L(1, y, z, t, ý, ż) 2. Now, transform the coordinate system to cylindrical coordinates: I = pcos o y = p sino so that you can write the Lagrangian and Lagrange's equations of motion for the particle in cylindrical coordinates - L(p, Ø, z, p, 0, 2).
Transcribed Image Text:Consider a particle of mass m moving in 3-dimensions in a force field of the form (as expressed in Cartesian coordinates): IX + vỹ + zż F(z, y, z) = K- (z2 + y? + z?)3/2' where K is a constant. 1. Write down the Lagrangian and Lagrange's equations of motion for this particle in Cartesian coordinates - L(1, y, z, t, ý, ż) 2. Now, transform the coordinate system to cylindrical coordinates: I = pcos o y = p sino so that you can write the Lagrangian and Lagrange's equations of motion for the particle in cylindrical coordinates - L(p, Ø, z, p, 0, 2).
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