ENAS Final Formula

# ENAS Final Formula - Useful Information and Formulas b a b...

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Useful Information and Formulas i b a u dv = uv | b a i b a v du sin2 α = 2sin α cos α x 2 + y 2 + z 2 + Gx + Hy + Iz + J = 0 d = r ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 + ( z 2 z 1 ) 2 b v b = r v 2 1 + v 2 2 + v 2 3 a sin α = b sin β = c sin γ c 2 = a 2 + b 2 2 ab cos γ proj b v = v · b b b b 2 b i j k u × v = u 1 u 2 u 3 v 1 v 2 v 3 n · ( r r 0 ) = 0 ax + by + cz + d = 0 2

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x = a cos t, y = a sin t, z = ct D = | ax 0 + by 0 + cz 0 + d | a 2 + b 2 + c 2 L = i b a r R R ± p dx dt P 2 + p dy dt P 2 + p dz dt P 2 dt L = i b a b d r dt b dt T ( t ) = r ( t ) b r ( t ) b N ( t ) = T ( t ) b T ( t ) b B ( t ) = T ( t ) × N ( t ) κ ( t ) = b T ( t ) b b r ( t ) b κ ( t ) = b r ( t ) × r ′′ ( t ) b b r ( t ) b 3 Δ r = i b a v ( t ) dt s = i b a b d r dt b dt = i b a b v ( t ) b dt v = ds dt T 3
a = d 2 s dt 2 T + κ p ds dt P 2 N a T = v · a b v b a N = b v × a b b v b κ = b v × a b b v b 3 r ( t ) = ( 1 / 2 gt 2 + s 0 ) j + t v 0 v 0 = ( v 0 cos α ) i + ( v 0 sin α ) j y = s 0 + (tan α ) x p g 2 v 2 0 cos 2 α P x 2 dw = f x dx + f y dy + f z dz dw dt = ∂w ∂x dx dt + ∂y dy dt + ∂z dz dt D u f ( x 0 , y 0 ) = f ( x 0 , y 0 ) · u F x ( x 0 , y 0 , z 0 )( x x 0 ) + F y ( x 0 , y 0 , z 0 )( y y 0 ) + F z ( x 0 , y 0 , z 0 )( z

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ENAS Final Formula - Useful Information and Formulas b a b...

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