A particle of mass m is projected upward with a velocity vo at an angle a to the horizontal in the uniform gravitational field of earth. Ignore air resistance and take the potential energy U at y=0 as 0. Using the cartesian coordinate system answer the following questions: a. find the Lagrangian in terms of x and y and identiy cyclic coordinates. b. find the conjugate momenta, identify them and discuss which are conserved and why c. using the lagrange's equations, find the x and y components of the velocity as the functions of time.
A particle of mass m is projected upward with a velocity vo at an angle a to the horizontal in the uniform gravitational field of earth. Ignore air resistance and take the potential energy U at y=0 as 0. Using the cartesian coordinate system answer the following questions: a. find the Lagrangian in terms of x and y and identiy cyclic coordinates. b. find the conjugate momenta, identify them and discuss which are conserved and why c. using the lagrange's equations, find the x and y components of the velocity as the functions of time.
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A particle of mass m is projected upward with a velocity vo at an angle a to the horizontal in the uniform gravitational field of earth. Ignore air resistance and take the potential energy U at y=0 as 0. Using the cartesian coordinate system answer the following questions:
a. find the Lagrangian in terms of x and y and identiy cyclic coordinates.
b. find the conjugate momenta, identify them and discuss which are conserved and why
c. using the lagrange's equations, find the x and y components of the velocity as the functions of time.
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