# Translational Dynamics

Settings to propagate the translational state of a body numerically can be created through the `translational()` factory function, described in detail in the API documentation. In the current page, only the Tudat-specific aspects of the input will be briefly described.

The default (conventional) representation for solving the translational equations of motion is by using the Cowell propagator (using Cartesian elements as the propagated states), but other formulations can be used (see below and Conventional vs. Propagated Elements).

## Inputs

In addition to the settings described here, the definition of translational dynamics settings requires:

Warning

The initial state must be provided in Cartesian elements, regardless of the propagator type

## Example

In the example below, the body “Spacecraft” will be propagated w.r.t. body “Earth” (also termed the ‘propagation origin’), using given acceleration models, a given initial state which defines the initial Cartesian state of the center of mass of “Spacecraft” w.r.t. the center of mass of “Earth”. A Runge Kutta 4 integrator is defined with step-size of 2 seconds. The propagation will terminate once the `simulation_end_epoch` termination condition is reached. The state will be propagated through the Encke formulation. Next to that, the propagator is asked to save the total acceleration. The time and state will be printed on the terminal once every 24 hours.

Required Show/Hide

```from tudatpy.kernel.numerical_simulation import propagation_setup
from tudatpy.kernel.astro import element_conversion
import numpy as np
```
```# Define central bodies
central_bodies = ["Earth"]

# Define bodies that are propagated
bodies_to_propagate = ["Spacecraft"]

# Define the acceleration models
# Define acceleration settings acting on spacecraft
accelerations_settings_spacecraft = dict( Sun=[propagation_setup.acceleration.point_mass_gravity()])
acceleration_settings = {"Spacecraft": accelerations_settings_spacecraft}
# Create acceleration models.
acceleration_models = propagation_setup.create_acceleration_models( bodies, acceleration_settings,
bodies_to_propagate,
central_bodies) ## BODIES MAYBE NEED TO BE ADDED? ##

# Define initial conditions
initial_state = [5.89960424e+06, 2.30545977e+06, 1.74910449e+06, -1.53482795e+03, -1.71707683e+03, 7.44010957e+03]
# Start of simulation
simulation_start_epoch = 9120 * constants.JULIAN_DAY

# Define numerical integrator (RK4; step size 2 seconds)
integrator_settings = propagation_setup.integrator.runge_kutta_4( 2.0 )

# Define termination settings
simulation_end_epoch = 9140 * constants.JULIAN_DAY
termination_settings = propagation_setup.propagator.time_termination(
simulation_end_epoch )

# Define propagator type
propagator_type = propagation_setup.propagator.encke

# Define dependent variables
dependent_variables_to_save = [propagation_setup.dependent_variable.total_acceleration( "Spacecraft" )]

# Define translational propagator settings
translational_propagator_settings = propagation_setup.propagator.translational(
central_bodies,
acceleration_models,
bodies_to_propagate,
initial_state,
simulation_start_epoch,
integrator_settings,
termination_settings,
propagator=propagator_type,
output_variables= dependent_variables_to_save,
print_interval=86400.0)
```