Fix two bugs in Targeter finite-difference corrector

[KonradStanski]

Summary

• Remove spurious .transpose() on VNC→inertial DCM in the convergence path of raphson_finite_diff.rs, which caused apply_with_traj() to fail verification on any VNC-frame targeting
• Move init_guess application outside the per-variable loop to prevent cumulative over-application (first variable's guess applied 3×, second 2×, third 1×), which caused verification failures on sensitive arcs even in inertial frame

Details

Bug 1 — DCM transpose: The convergence branch (building corrected_state from xi_start + total_correction) transposed the dcm_to_inertial rotation matrix at line ~549, effectively rotating inertial→VNC instead of VNC→inertial. All three other call sites in the same file (init guess application, Jacobian perturbation, iteration step) use the DCM without transpose.

Bug 2 — Init guess double-counting: state_correction was applied to xi inside the for (i, var) loop. With 3 velocity variables [vx, vy, vz]:

• After variable 0: xi.vel += [vx, 0, 0]
• After variable 1: xi.vel += [vx, vy, 0] (accumulated) → total [2·vx, vy, 0]
• After variable 2: xi.vel += [vx, vy, vz] → total [3·vx, 2·vy, vz]

But total_correction correctly stores [vx, vy, vz], so the convergence path's corrected_state disagrees with the iterated xi. The fix moves application outside the loop, matching the pattern already used in the iteration loop (~lines 608-729).

Neither bug manifests when init_guess = 0 (the default from Vary::into()), which is why existing tests pass. Both bugs trigger on sensitive, long-arc targeting with nonzero initial guesses (e.g., trans-lunar injection).

Test plan

• All 83 existing cargo test --lib tests pass
• Verified with a trans-lunar injection scenario (HEO → lunar flyby): Nyx Targeter now converges in 4 iterations with apply_with_traj verification passing

Closes #525

🤖 Generated with Claude Code

[gemini-code-assist]

Code Review

This pull request refactors the initial guess application in the Raphson finite difference targeter by accumulating state corrections and applying them once after the loop, and corrects a matrix calculation by removing an unnecessary transposition. Feedback indicates that the new !finite_burn_target check should be removed to ensure consistency with the main iteration loop, allowing impulsive state corrections to be applied even when finite burn variables are present.

[ChristopherRabotin]

Suggested change

	// the pattern used in the iteration loop at lines ~608-729).
	// the pattern used in the iteration loop).

I prefer not referring specific line numbers in comments.