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Unformatted text preview: m in 3-D Cartesian space is trapped in a plasma field which exerts an applied conservative force k z F ˆ β-= , for which the potential energy is 2 2 1 z V = , under the nonholonomic constraint ) ( =-+ z y x x . The generalized coordinates in the 3-D Cartesian space are ( x, y, z ), and the position vector is k z j y i x r ˆ ˆ ˆ + + = . Treat x as the dependent coordinate (i.e. x is the dependent generalized velocity, while y and z are the independent generalized velocities). Find the equation of motion corresponding to z , using the method of your choice. Neglect gravity. (You do not need to eliminate x from the final answer, if it shows up.)...
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- Spring '07
- Force, 3-D Cartesian space, generalized force Qθ