Notes_03_03

Notes_03_03 - Notes_03_03 page 1 of 4 Newton-Raphson...

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Unformatted text preview: Notes_03_03 page 1 of 4 Newton-Raphson Algorithm x k+1 = x k- f k / ( ∂ f/ ∂ x) k Example : x 2- 4x + 1 = 0 Use: f(x) = x 2- 4x + 1 ∂ f/ ∂ x = 2x - 4 x f(x) 1 1-2 2-3 3-2 4 1 5 6 k x f(x) ∂ f/ ∂ x f / ( ∂ f/ ∂ x) 1 5 2 3 4 5 1 2.5 2 3 4 5 1 1 2 3 4 5 6 1 4 2 3 5-1-2-3 6 6 1 4 1 4 0.25 3.75 0.0625 3.5 0.01786 3.7321 0.0003 3.4643 0.00009 3.7320-2.75 1-2.75 5.25 7.5625 6.5 1.1635 4.0865 1.3536 4.1731 0.3244 3.7622 0.1052 3.5243 0.0299 3.7323-2-2 1 1-4-0.25 0.25 0.0625-3.5-0.01786 0.2679 0.00017-3.4642-0.00005 0.2679 Notes_03_03 page 2 of 4 Newton-Raphson for Four Bar Given: constants r 1 r 2 r 3 r 4 θ 1 and variable θ 2 Find: θ 3 and θ 4 Subject to: cos r cos r cos r cos r f 1 1 4 4 3 3 2 2 H = θ- θ- θ + θ = sin r sin r sin r sin r f 1 1 4 4 3 3 2 2 V = θ- θ- θ + θ = Use: { } θ θ = 4 3 q generalized coordinates, { } = Φ V H f f constraint functions Taylor series about estimate {q} k : θ...
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This document was uploaded on 02/10/2011.

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Notes_03_03 - Notes_03_03 page 1 of 4 Newton-Raphson...

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