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Unformatted text preview: σ = σ ∗ , τ = τ ∗ . 1 3. The relationship between the coordinates of a tangent vector relative to the cartesian and cylindrical coordinate charts is x y z = ρ cos ϕ − ϕ ρ sin ϕ ρ sin ϕ + ϕ ρ cos ϕ h The relationship between the coordinates of the tangent vector on b C relative to the chart ³ b C , ( y,z ) T ´ and the correspondint tangent vector on C relative to the Cartesian coordinate chart is x y z = y − 2 z y z 4. The virtual power is given by F x x + F y y = R ( F x cos θ + F y sin θ ) θ = F θ θ , such that F x /F y = − tan θ ⇒ F θ = 0 which states that a force pointing towards O has no virtual power, since it is orthogonal to the motion of the particle. 5. 2...
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 Spring '08
 Weaver
 Manifold, Inverse function, τ, Mechanical Science and Engineering, tangent vector

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