Question

- If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange’s Equations of motion show by direct substitution that:

L’ = L +
dF(q_{1},q_{2},…q_{n},t)/dt
also satisfies Lagrange’s equation
where F is any arbitrary, but differentiable function of its
arguments.

Answer #1

Suppose the representative consumer’s preferences are given by
the utility function,
U(C, l) = aln C + (1- a) ln l
Where C is consumption and l is leisure, with a utility
function that is increasing both the arguments and strictly
quiescence, and twice differentiable.
Question:
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Your task will be to derive the equations describing the
velocity and acceleration in a polar coordinate
system and a rotating polar vector basis for an object in general
2D motion starting from a general
position vector. Then use these expressions to simplify to the case
of non-uniform circular motion, and
finally uniform circular motion.
Here's the time-dependent position vector in a Cartesian coordinate
system with a Cartesian vector
basis: ⃗r(t)=x (t)
̂
i+y(t)
̂
j where x(t) and y(t)...

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