Generic zero-order-hold leg

pykep_core::leg::ZohLeg transcribes a transfer between two fixed endpoint states as non-uniform segments with continuous, piecewise-constant controls. It is generic over any Rust model implementing ZeroOrderHoldModel; aliases cover every built-in ZOH dynamics family:

The units and frame conventions of each row are those of its model in zero-order-hold.md. c is the normalized mass-flow coefficient for the three low-thrust models and the normalized lightness coefficient for the solar sail.

Grid, controls, and cut

For S segments, construction requires exactly S + 1 finite, strictly-increasing time-grid nodes and S finite control vectors. Controls are stored in chronological order and own the half-open interval [time_grid[i], time_grid[i+1]); the final endpoint belongs to the final segment.

The cut uses the same convention as the upstream leg:

forward_segments = floor(S * cut)
backward_segments = S - forward_segments

The forward state starts at the initial endpoint and the backward state starts at the final endpoint. The mismatch is their component-wise difference at the cut. Cuts zero and one are supported without special placeholder states.

The leg is immutable after construction. It rejects invalid endpoint states, model constants, dimensions, grids, cuts, tolerances, maximum steps, and maximum-step magnitudes before evaluation.

mismatch_constraints() preserves the established DOP853 propagation. Built-in models additionally provide mismatch_constraints_with_method(IntegrationMethod), so repeated derivative-free objective evaluations can select the accelerated Taylor backend explicitly.

Sensitivity layout

mismatch_jacobian() returns four output-by-input matrices:

Each segment propagates a local state-transition and active-control matrix. The leg composes those matrices from each side of the cut and includes the dynamics jump at every switching time. Constant model parameters are fixed leg configuration and therefore are not a returned derivative group.

The four built-in models compute their local RHS Jacobians with fixed-size centered differences using a relative step of 3e-6. Consequently, integrator tolerances such as 1e-12 do not imply 1e-12 derivative accuracy: the pinned end-to-end validation uses scaled tolerances up to 3e-5. See zero-order-hold.md for the model-level contract and validation evidence.

Integration and failures

IntegratorOptions applies independently to every segment, including relative and absolute tolerances, optional initial and maximum step sizes, maximum steps, and maximum rejections. A propagation failure is reported as an IntegrationFailure containing the direction, chronological segment index, and attempted time interval.

state_history(samples_per_segment) uses one DOP853 dense solve per segment for uniformly spaced states including both endpoints. state_history_with_method(samples_per_segment, IntegrationMethod) selects DOP853 or Taylor for built-in models. DOP853 backward segments are evaluated through the equivalent increasing coordinate tau = segment_start - time to avoid a decreasing-time dense-output boundary issue in the numerical backend; Taylor supports the decreasing grid directly. At least two samples are required. Backward histories list the final segment first, matching propagation order. evaluate_zoh_mismatch_batch() evaluates validated Rust legs in input order.

Python

pykep_rust.ZohLeg accepts a ZohModel value: Kepler, Cr3bp, Equinoctial, or SolarSail. The constructor validates dynamic state, control, and constant dimensions for that selection. Mismatch, Jacobian, and history evaluation release the Python GIL.

The ZOH-leg batch methods clone the small immutable leg descriptors, release the GIL once, and return results in input order. workers=0 uses the shared pool, workers=1 is serial, and a larger value selects a cached pool of that exact size.