Claude Skills by ashfordeOU

Use when you must compute the collision-course intercept geometry for a constant-speed pursuer against a constant-velocity target: the lead angle of the pursuer velocity off the line of sight that closes the collision triangle, the closing speed along the line of sight, the time to go to the predicted intercept point, the intercept point coordinates, and the bearing error check against the current pursuer heading. Produces the lead angle, closing speed, time to go, intercept point, and the he...

Use when you must compute a command to line of sight guidance command for a missile intercept: derive the tracker to target line of sight angle, the angular deviation of the missile from the tracker target line, the line of sight rotation rate, the steering acceleration proportional to the LOS error and its rate, the signed cross track offset of the missile from the line, and the on line verdict that gate a CLOS guidance assessment. Produces the LOS angle, wrapped LOS error, LOS rate, steerin...

Use when you must plan a boustrophedon area-coverage search path for a fixed-wing UAS or rotorcraft over a rectangular survey region: compute the ground swath width from the sensor cross-track field of view and altitude, derive the track spacing from the required side overlap, lay out the alternating lawnmower passes, add the 180 degree half-circle turns at the vehicle turn radius, and sum the total path length and survey time at cruise speed. Produces the swath width, track spacing, pass cou...

Use when you must plan the shortest fixed wing path between two heading constrained poses with Dubins curves: compute the left and right arc centers for the minimum turn radius, find the outer or inner tangent points between the turn circles, form the six CSC and CCC path families (RSR, LSL, RSL, LSR, RLR, LRL), and select the minimum length path. Produces the Dubins path type, total length, segment lengths, arc centers, and waypoints that gate UAS path planning and waypoint guidance. Trigger...

Use when you must compute the impact-angle-control-guidance command for a planar intercept against a stationary target with a commanded terminal flight path angle: the collision-course nulling baseline from the crossrange offset, the crossrange velocity and the time to go, the terminal crossrange velocity that realizes the commanded impact angle, the impact-angle error between the commanded terminal flight path angle and the current flight path angle, and the impact-angle-error-feedback bias ...

Use when a task asks where a round will land, how long the ballistic flight lasts, or how launch speed and flight path angle errors displace the impact point. Compute the ballistic impact point prediction for a projectile from launch position, launch speed, and flight path angle: determine the flat earth vacuum range with the range equation, the time of flight, the impact coordinates from the launch point and heading, and the sensitivity of the landing point to initial condition errors. Trigg...

Use when you must compute the impact-time-control-guidance command for a salvo or simultaneous-impact engagement: the proportional-navigation baseline acceleration from the closing speed and the line of sight rate, the PNG time-to-go estimate on the collision course, the impact-time error between the commanded remaining time to go and the natural PNG time, and the time-to-go-error-feedback bias that lengthens or shortens the intercept path so the group arrives at the commanded impact time. Pr...

Use when a task asks how to reach an intermediate condition before final intercept, how much speed remains to be gained, or when to hand off to terminal guidance. Shape the midcourse flight of an interceptor or guided vehicle between launch and terminal handover: steer through a planned waypoint with a turn-rate-limited heading law, compute the velocity-to-be-gained speed deficit along the desired course, evaluate the zero-effort-miss of the closing geometry, size the handover condition that ...

Use when you must compute the proportional navigation guidance command for a planar intercept in SI units: determine the closing velocity from the relative position and velocity vectors, compute the line of sight rate, and calculate the commanded acceleration perpendicular to the line of sight from the navigation constant. Produces range, closing velocity, LOS rate, and the acceleration command that gate an intercept guidance assessment. Trigger: proportional navigation, line of sight rate, c...

Use when you must compute pursuit guidance commands for a planar intercept: derive the line of sight angle, the pure pursuit heading that points the interceptor velocity at the target, the wrapped guidance error between the current heading and the aim heading, the lead angle for a lead pursuit collision course, and the capture condition from the interceptor to target speed ratio. Produces the pursuit aim heading, guidance error, lead angle, capture feasibility, intercept time, and the proport...

Use when you must locate a stationary emitter from passive angle-of-arrival bearing lines measured at known observer positions. Build the linearized bearing equations sin(beta_i)*(x - xi) - cos(beta_i)*(y - yi) = 0 per observer, solve the Stansfield closed-form weighted least squares for the two-dimensional emitter fix with an equal-angle first pass and a distance-weighted second pass, and read the fix covariance error ellipse plus the per-bearing residual angles. Produces the emitter positio...

Use when you must evaluate GNSS positioning accuracy from satellite geometry: build the geometry matrix H from satellite line-of-sight unit vectors, form the normal matrix H^T H, invert it, and read the dilution of precision values (GDOP, PDOP, HDOP, VDOP, TDOP) off the diagonal. Applies to GPS/GNSS receiver analysis, elevation mask studies, and satellite subset selection. Produces the DOP values, the 1-sigma position error from a user equivalent range error, the elevation mask filter, and th...

Use when you must smooth GNSS code pseudoranges with carrier-phase delta ranges before positioning: run the first-order Hatch recursion at a smoothing time constant, carry the smoothed range between epochs on the precise carrier increments, and monitor the code-carrier ionospheric divergence whose trailing-window slope fit predicts the smoothed-minus-code bias that would alarm a diverging range. Computes the noise-reduction verdict from the exact steady-state code-noise closed form sigma_code...

Use when you must estimate the 3-D velocity of a GNSS receiver and its receiver clock drift at a single epoch from carrier-phase delta-range-rate (doppler) observables: propagate each satellite ECEF position and velocity from the broadcast-ephemeris Kepler elements, form the line-of-sight unit vector from the receiver position (pseudorange fix first, or supplied), predict the range rate rho_dot = (v_sat - v_rec) dot u + c*dt_dot, and solve the iterated least-squares system over the per-satell...

Use when you must compute a GNSS receiver position fix from pseudorange measurements: given satellite positions in ECEF and their pseudoranges (geometric range plus receiver clock bias), solve the four-unknown navigation equations for x, y, z and clock bias with an iterated least-squares adjustment and 4x4 normal equation solves. Produces the converged ECEF position, clock bias, post-fit residuals with RMS, and post-fit position error from the geometry matrix. Requires at least four satellite...

Use when you must run receiver autonomous integrity monitoring (RAIM) fault detection and exclusion on an overdetermined GNSS pseudorange measurement set: build the geometry matrix H from satellite line-of-sight unit vectors, solve the overdetermined least-squares navigation solution, form the residual test statistic and compare it against a chi-square threshold at 1e-5 false-alarm probability, compute the horizontal protection level from the worst-case satellite slope, and identify the fault...

Use when you must compute the position of a GNSS rover relative to a fixed base station from double-difference carrier-phase observables: form the per-satellite single differences across the receivers at each epoch of a common-view observation arc, then the double differences across satellite pairs and epochs, and solve the stacked least-squares normal equations for the float baseline and the per-pair float ambiguities. Resolve the integer ambiguities by rounding candidate sets around the flo...

Use when you must assess an inertial navigation system (INS): estimate position error growth from accelerometer bias and gyro drift, check the Schuler period and the leveling response, compare strapdown and gimbaled mechanization, and scope alignment and INS/GPS integration. Produces the double-integration position error from an accelerometer bias, the cubic position error from gyro drift, the bounded Schuler steady-state offset, and the Schuler period and frequency. Trigger: inertial navigat...

Use when you must fuse INS and GNSS in a loosely coupled error-state integration filter: assemble the 5-state psi-angle error model of the horizontal INS drift from the specific forces, discretize it into the state transition matrix, predict the position, velocity and heading error states and their covariance between GNSS fixes, and apply the GNSS position measurement update that drives the estimated error state toward the innovation through the Kalman gain. Produces the error-state matrix, t...

Use when you must correct the L1 pseudorange for the broadcast ionospheric delay: apply the klobuchar-broadcast-model to the user position and the satellite line of sight, compute the geomagnetic latitude of the ionospheric pierce point from the earth-centred angle and the azimuth, evaluate the amplitude and period quartic polynomials in the broadcast alpha and beta coefficients at that geomagnetic latitude, form the vertical delay from the 5 ns base and the day-curve shape about the 14:00 lo...

Use when you must design or run a discrete-time Kalman filter for single-axis state estimation in SI units: predict the state and its error covariance through the dynamics model, compute the innovation and innovation variance, calculate the Kalman gain, and correct the state and covariance from a noisy measurement. Produces the predicted and corrected states, the error covariance, the Kalman gain, and the innovation sequence that gate a navigation or estimation assessment. Trigger: kalman fil...

Use when you must convert navigation coordinate frames for an aircraft or spacecraft: transform geodetic latitude, longitude, and altitude on the WGS-84 ellipsoid into ECEF position, build the ECEF to NED rotation matrix at a reference point, resolve velocity into north, east, and down components, and compute the Earth rotation angle from a Julian date for inertial to Earth-fixed frames. Produces ECEF coordinates in meters, the NED rotation matrix, NED velocity, and GMST rotation angle in rad...

Use when you must aid an unaided inertial navigation solution from terrain with no GNSS available: correlate a measured radar-altimeter terrain profile (INS altitude minus radar clearance) along the INS indicated track against a stored digital elevation model strip, form the TERCOM correlation surface over the candidate along-track and cross-track offsets, and take the best-match offset as the coarse position correction. Then run the point-mass SITAN fine stage, per-mass terrain-height likeli...

Use when you must run a tightly-coupled-ins-gnss integration filter: propagate the eight INS error states (3 position error, 3 velocity error, receiver clock bias in metres, clock drift in m/s) of the constant-velocity-error model between epochs, predict each raw pseudorange from the inertial position estimate plus the clock bias state, build the measurement matrix from the line-of-sight geometry rows with the unit clock column, and apply the raw-pseudorange-update Kalman correction on the re...

Use when you must correct the GNSS range for the tropospheric delay: evaluate the saastamoinen-model delay from the surface pressure, temperature and water-vapour partial pressure, form the gravity and height factor from latitude and station height, form the zenith-hydrostatic-delay by dividing the pressure by that factor, form the zenith-wet-delay from the water-vapour partial pressure and the temperature term, sum both into the zenith total delay and map it to the slant-tropospheric-delay w...

Use when you must compute the time-optimal bang-bang control of a double integrator: the switching curve s = x + v|v|/(2a), the bang-bang command u = -a*sign(s) under a hard input limit |u| <= a, the exact rest-to-rest maneuver time T* = 2*sqrt(d/a), the switch point at half distance with velocity -sqrt(a*d), and the general minimum-time trajectory for nonzero initial velocity. Produces the switch point, the command profile and the maneuver time for single-axis attitude slew and translation b...

Use when setting up and assessing pseudospectral trajectory optimization with Dymos: plan optimal-control problems as phases with collocation nodes, check that phase setup includes initial-state and final bounds plus an objective, and verify convergence, state continuity across segments, and total delta-v against expected budgets for ascent or orbit-transfer trajectories. Flags under-resolved phases (fewer than 5 nodes), unconverged runs, and discontinuities at segment boundaries. Trigger: tr...

Use when you must run iterative LQR / differential dynamic programming (ilqr-ddp) on a nonlinear discrete-time system: roll the nominal control forward through the two-state soft-landing dynamics under gravity and quadratic drag, run the backward Riccati pass that forms the value-function quadratics Qx, Qu, Qxx, Qux, Quu and the local affine control law u = ubar + K(x - xbar) + k at each step, and execute the forward pass with backtracking line search and regularization until the total cost c...

Use when you must run loop-transfer-recovery on the LQG loop of the two-state plant family: inflate the filter process noise weight q on the driven input channel through Qw(q) = Qw0 + q^2 B B^T, re-solve the filter Riccati equation for the error covariance and the estimator gain at every q, and compare the recovered output loop transfer function with the full-state target loop on a log-spaced frequency grid until the grid-max mismatch M(q) falls at or below the recovery tolerance. Produces th...

Use when you must design a linear-quadratic-Gaussian output-feedback compensator for a two-state system whose state is not fully measurable: solve the regulator algebraic Riccati equation for the symmetric stabilizing P and the gain K from the quadratic cost weights, solve the filter (Kalman) algebraic Riccati equation for the error covariance S and the estimator gain L from the process and measurement noise covariances, assemble the dynamic output-feedback compensator state-space realization...

Use when you must design an LQR state-feedback gain matrix for a scalar-input two-state system such as spacecraft attitude control: solve the algebraic Riccati equation for the cost weights, compute the gain matrix, verify closed-loop stability of the regulated system, and assess the Q over R weighting trade. Produces the Riccati solution, the gain vector, and the stability verdict that feed the control-law design. Trigger: lqr, linear quadratic regulator, riccati equation, gain matrix, state...

Use when you must design a model predictive control (MPC) receding horizon controller for a linear discrete time system such as a double integrator: choose the finite horizon quadratic cost with prediction horizon and control horizon, enforce input constraints and state constraints, and run a closed loop simulation. Produces the first optimal control move from the small dense quadratic program, solved deterministically without scipy, plus the feasibility verdict. Trigger: mpc, model predictiv...

Use when the task is spacecraft attitude dynamics, rotational kinematics, or momentum management for ADCS dynamics analysis and simulation. Model spacecraft attitude dynamics with the Euler rotational equations of motion: propagate quaternion kinematics from angular velocity, integrate the inertia tensor and applied torques into angular rates, and compute angular momentum, torque-free nutation, gravity-gradient torque, and momentum wheel effects. The stdlib logic is deterministic and offline:...

Use when you must determine an initial orbit from three inertial position vectors: run the Gibbs method to recover the velocity at the central observation, apply the Herrick-Gibbs finite-difference method when the vectors are closely spaced, and convert the state to classical orbital elements with the vis-viva energy consistency check. Produces the central velocity, the classical elements (a, e, i, RAAN, argp, nu), the chosen method verdict and the orbit-fit verdict. Trigger: orbit-determinat...

Use when analyzing spacecraft orbital mechanics with two-body and J2-perturbed motion: compute velocities with the vis-viva equation, size Hohmann transfer delta-v and transfer time between coplanar circular orbits, and sanity-check LEO-to-GEO transfer budgets (about 3.9 km/s total delta-v). Flags nodal-regression drift from J2 that exceeds an allowed rate for orbit maintenance planning. Uses Earth gravitational parameter 3.986004418e14 m^3/s^2. Trigger: orbit, orbital mechanics, hohmann tran...

Use when you must plan an orbital rendezvous phasing maneuver: compute the drift rate needed to cover a phase angle in a transfer time, size the phasing delta-v around a circular orbit, and check the closing rate against the allowed value. Produces the drift rate, the delta-v estimate, and the closing rate verdict that gate the maneuver plan. Trigger: rendezvous, phasing orbit, closing rate, orbital maneuver, delta-v, chase.

Use when a task concerns aerospace manufacturing and quality management: guide the router to the manufacturing-quality pack. AS9100 quality, nonconformance-control, supplier-control, counterfeit-prevention, calibration-control, corrective-action, document-control, and statistical-process-control cover QMS scoping, disposition, supplier risk, counterfeit scoring, calibration, CAPA closure, controlled documents, and SPC; first-article-inspection, delta-fai, and fai-revalidation cover AS9102 FAI...

Use when qualifying a powder bed fusion or directed energy deposition build, when a build parameter change needs energy density re-verification, or when preparing the AM qualification record and witness coupon plan. Define and validate the additive manufacturing process parameter set for aerospace parts: record the layer height, laser power, scan speed, and hatch spacing, compute the volumetric energy density from those four build parameters, size the witness coupon sample plan for material p...

Use when developing LPBF process parameters, mapping energy density to melt pool regime, screening keyhole mode risk, or sizing the parameter development matrix for a powder bed fusion build. Develop the laser powder bed fusion (LPBF) parameter window: compute the volumetric energy density from laser power, scan speed, hatch spacing, and layer thickness, check hatch overlap between melt tracks, classify the process window as conduction mode, transition, or keyhole mode with porosity expectati...

Use when you must design an attribute acceptance sampling plan: choose the sample size code letter from the lot size and the inspection level, look up the single-sampling plan (sample size n, accept number Ac, reject number Re) for the required AQL from a small embedded reference table, decide accept or reject from the number of nonconforming units found in the sample, and compute the operating-characteristic probability of acceptance across incoming fraction nonconforming with the binomial m...

Use when you must analyze inspector agreement on attribute judgments: percent agreement on go/no-go or accept/rework/reject results, the Cohen kappa for two inspectors and the Fleiss kappa for three or more inspectors with the chance-agreement correction, the kappa verdict against the attribute measurement system acceptance bands (0.75 and up good, 0.40 to 0.75 marginal, under 0.40 poor), and the retraining or study rework flag when agreement is poor. Produces observed agreement, chance agree...

Use when you must build attribute control charts for conformance and defect count data: the p-chart for fraction nonconforming of subgroups with constant sample size, the np-chart for count nonconforming, the c-chart for defect counts per constant inspection area, and the u-chart for defect counts per unit with variable inspection area. Computes the grand average, the 3-sigma control limits from the binomial or Poisson normal-approximation standard error, floors the lower limit at zero, flags...

Use when you must control calibration of inspection, measuring, and test equipment under an AS9100-style QMS: determine the test accuracy ratio (TAR, 4:1 guidance) between the calibration standard and the unit under test, judge calibration due dates and overdue instruments, check a measured value against nominal and tolerance, and decide recall versus review when a calibrated standard drifts out of tolerance. Covers the calibration system (who calibrates, traceability to national standards), ...

Use when you must drive a corrective action (CAPA) record for a manufacturing nonconformance to closure: run the eight-discipline (8D) problem-solving workflow, check that a containment action is recorded, validate the five-whys root cause chain, and confirm the corrective action and the effectiveness evidence before the record closes. Produces the closure stage verdict, the missing items, and the effectiveness pass or fail that gate the nonconformance closure. Trigger: corrective action, cap...

Use when you must plan counterfeit parts prevention for an aerospace procurement: score the counterfeit risk from the sourcing and verification controls in place, decide whether reporting is required, and confirm the procurement control set is complete per AS9100 practice. Produces the risk level, the reporting trigger, and the control completeness verdict that gate procurement release. Trigger: counterfeit prevention, counterfeit parts, procurement control, as9100, supply chain, incoming ins...

Use when you must monitor a production process for small sustained mean shifts: compute the tabular CUSUM path (upper S+ and lower S- statistics from standardized deviations with slack k and decision interval h) and the first signal sample, run the EWMA recursion with per-sample time-varying sigma limits (lambda weighting, L-sigma UCL/LCL) and its first signal sample, and combine both charts into one monitoring verdict that catches small shifts a single-point check misses. Produces the CUSUM ...

Use when you must control aerospace manufacturing documents: maintain the master list of controlled documents, check that a document is approved before issue, confirm that the shop floor copy is at the current revision, and disposition obsolete revisions by removing them from active use while retaining them in the register as history. Produces the register validity verdict, the use verdict for a copy, and the obsolete disposition that gate document control. Trigger: document control, master l...

Use when you must audit a foreign object debris (FOD) prevention program for aerospace production: classify the FOD zone from the part criticality and debris exposure, compute the FOD risk score, derive the FOD sweep interval and the tool-control and housekeeping controls for the zone, reconcile the issued tool count against the returned tools, and score the program against the required control set for the audit verdict with findings. Produces the zone class, the risk score, the sweep interva...

Use when you must run the gage bias and linearity study: compute the per-level bias and the overall mean bias from reference masters and measured biases, fit the least-squares regression of bias on the reference value returning the slope, intercept, residual sum of squares and R-squared as the linearity evidence, test the mean bias for significance against the two-sided 95 percent t critical at the study degrees of freedom, and apply the percent-of-reference acceptability band per level. Prod...

Use when you must run the ANOVA estimator for a gage repeatability and reproducibility study: decompose total variation of replicated balanced readings into part, operator, part-by-operator interaction and equipment sums of squares, estimate variance components with the non-negative interaction floor, compute equipment, appraiser, interaction, combined GRR, part and total variation, the percent GRR verdict on the 10/30 acceptance bands, part and interaction F statistics, and the number of dis...