a methodology to repair or deorbit leo satellite constellations - AGI

42∆ ̇ ∆ ̇ [ ( )∆ ∆ ̇ ( )∆ ̇ ]which simplifies to become:∆ ̇ ( )∆ ∆ ̇ ( )∆ ̇ (2.36)Integrating this expression with respect to time, we find that:∆ . / ∆ ∆ ̇ . / ∆ ̇ (2.37)Evaluating ∆y atyields:Formatted: Font: 12 pt∆ ∆ ̇ → ∆ ∆ ̇Substituting this value for C into equation Equation (2.37), we get:∆ ( )∆ ∆ ( )∆ ̇ . / ∆ ̇ (2.38)Finally, the solution of equation Equation (2.28c) is:∆ (2.39)so that∆ ̇ (2.40)We evaluate the two expressions atto obtain the constants of integration:Formatted: Font: 12 pt∆∆ ̇Putting these values for D and E back into equation Equation (2.38) and Eequation(2.40) yields:∆ ∆ ∆ ̇ (2.41)∆ ̇ ∆ ∆ ̇ (2.42)