vamseeachanta Scipy Method (+2)
Scipy Method
1. Define objective function: residual = current_tension - target_tension
2. Optimization variables: line lengths
3. scipy.optimize.fsolve minimizes residuals
4. Length changes distributed across sections proportionally
Newton-Raphson Method
1. Calculate Jacobian: J[i,j] = ∂T_i/∂L_j
2. Calculate residuals: r_i = T_current_i - T_target_i
3. Solve: J × ΔL = -r
4. Update: L_new = L_old + damping × ΔL
5. Repeat until convergence
EA-Based Method
1. From catenary theory: ΔL ≈ ΔT × L / EA
2. Calculate tension error: ΔT = T_current - T_target
3. Calculate length change: ΔL = ΔT × L / EA
4. Apply with damping
5. Repeat until convergence