Class of test problem of free fall in air resistance. More...

#include <num_prob_collect/ode/free_fall_in_resistance_problem.h>

Collaboration diagram for num_prob_collect::ode::free_fall_in_resistance_problem:

Public Types
using	jacobian_type = Eigen::Matrix2d
	Type of Jacobian.

using	scalar_type = double
	Type of scalars.

using	variable_type = Eigen::Vector2d
	Type of variables.

Public Member Functions
	free_fall_in_resistance_problem (scalar_type k, scalar_type g)
	Constructor.

auto	diff_coeff () const noexcept -> const variable_type &
	Get the differential coefficient.

void	evaluate_on (scalar_type, const variable_type &variable, num_collect::ode::evaluation_type)
	Evaluate on a (time, variable) pair.

auto	jacobian () const noexcept -> const jacobian_type &
	Get the Jacobian.

Static Public Attributes
static constexpr auto	allowed_evaluations
	Allowed evaluations.

Private Attributes
variable_type	diff_coeff_ {}
	Differential coefficient.

scalar_type	g_
	Gravity.

jacobian_type	jacobian_ {}
	Jacobian.

scalar_type	k_
	Coefficient of resistance.

Detailed Description

Class of test problem of free fall in air resistance.

This solves the following equation of motion:

\[ \ddot{x} = -k \dot{x} - g \]

Here, k and g are constants.

In this class, the following equation is used to solve the above equation:

\[ \frac{d}{dt} \begin{pmatrix} \dot{x} \\ x \end{pmatrix} = \begin{pmatrix} -k \dot{x} - g \\ \dot{x} \end{pmatrix} \]

When the initial variable is (0, 0), the solution is the following:

\[ \begin{pmatrix} \dot{x} \\ x \end{pmatrix} = \begin{pmatrix} \frac{g}{k}e^{-kt} - \frac{g}{k} \\ -\frac{g}{k^2}e^{-kt} - \frac{g}{k}t + \frac{g}{k^2} \end{pmatrix} \]

Definition at line 53 of file free_fall_in_resistance_problem.h.

Member Typedef Documentation

◆ jacobian_type

using num_prob_collect::ode::free_fall_in_resistance_problem::jacobian_type = Eigen::Matrix2d

Type of Jacobian.

Definition at line 62 of file free_fall_in_resistance_problem.h.

◆ scalar_type

using num_prob_collect::ode::free_fall_in_resistance_problem::scalar_type = double

Type of scalars.

Definition at line 59 of file free_fall_in_resistance_problem.h.

◆ variable_type

using num_prob_collect::ode::free_fall_in_resistance_problem::variable_type = Eigen::Vector2d

Type of variables.

Definition at line 56 of file free_fall_in_resistance_problem.h.

Constructor & Destructor Documentation

◆ free_fall_in_resistance_problem()

num_prob_collect::ode::free_fall_in_resistance_problem::free_fall_in_resistance_problem	(	scalar_type	k,
		scalar_type	g )

inline

Constructor.

Parameters

[in]	k	Coefficient of resistance.
[in]	g	Gravity.

Definition at line 74 of file free_fall_in_resistance_problem.h.

Member Function Documentation

◆ diff_coeff()

auto num_prob_collect::ode::free_fall_in_resistance_problem::diff_coeff ( ) const -> const variable_type&

inlinenodiscardnoexcept

Get the differential coefficient.

Returns: Differential coefficient.

Definition at line 95 of file free_fall_in_resistance_problem.h.

◆ evaluate_on()

void num_prob_collect::ode::free_fall_in_resistance_problem::evaluate_on	(	scalar_type	,
		const variable_type &	variable,
		num_collect::ode::evaluation_type	)