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<tr id="row_0_16_87_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_random_source.html" target="_self">RandomSource</a></td><td class="desc">A source block which generates random numbers at a fixed sampling interval, with a zero-order hold between samples </td></tr>
<tr id="row_0_16_89_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_runge_kutta3_integrator.html" target="_self">RungeKutta3Integrator</a></td><td class="desc">A third-order Runge Kutta integrator with a third order error estimate </td></tr>
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<tr id="row_0_16_90_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html" target="_self">RungeKutta5Integrator</a></td><td class="desc">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fourth order error estimate </td></tr>
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<tr id="row_0_16_90_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html" target="_self">RungeKutta5Integrator</a></td><td class="desc">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fifth order error estimate </td></tr>
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<tr id="row_0_16_91_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_saturation.html" target="_self">Saturation</a></td><td class="desc">An element-wise hard saturation block with inputs signal <code>u</code>, saturation values \( u_{min} \) and/or \( u_{max} \), and output <code>y</code> respectively as in: </td></tr>
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<tr id="row_0_16_92_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_scalar_dense_output.html" target="_self">ScalarDenseOutput</a></td><td class="desc">A <a class="el" href="classdrake_1_1systems_1_1_dense_output.html" title="An interface for dense output of ODE solutions, to efficiently approximate them at arbitrarily many p...">DenseOutput</a> class interface extension to deal with scalar ODE solutions </td></tr>
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<tr id="row_0_16_93_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_scalar_initial_value_problem.html" target="_self">ScalarInitialValueProblem</a></td><td class="desc">A thin wrapper of the <a class="el" href="classdrake_1_1systems_1_1_initial_value_problem.html" title="A general initial value problem (or IVP) representation class, that allows evaluating the 𝐱(t; 𝐤) sol...">InitialValueProblem</a> class to provide a simple interface when solving scalar initial value problems i.e </td></tr>
</pre><p>If the integrator does not provide an error estimate, the derived class implementation should return 0. </p>
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<p>Implemented in <aclass="el" href="classdrake_1_1systems_1_1_velocity_implicit_euler_integrator.html#a447328b1aaa3ed12450855b792983d24">VelocityImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_implicit_euler_integrator.html#a447328b1aaa3ed12450855b792983d24">ImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_semi_explicit_euler_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">SemiExplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_radau_integrator.html#a447328b1aaa3ed12450855b792983d24">RadauIntegrator< T, num_stages ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta3_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">RungeKutta3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">RungeKutta5Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_bogacki_shampine3_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">BogackiShampine3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_explicit_euler_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">ExplicitEulerIntegrator< T ></a>, and <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta2_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">RungeKutta2Integrator< T ></a>.</p>
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<p>Implemented in <aclass="el" href="classdrake_1_1systems_1_1_velocity_implicit_euler_integrator.html#a447328b1aaa3ed12450855b792983d24">VelocityImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_implicit_euler_integrator.html#a447328b1aaa3ed12450855b792983d24">ImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_semi_explicit_euler_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">SemiExplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_radau_integrator.html#a447328b1aaa3ed12450855b792983d24">RadauIntegrator< T, num_stages ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">RungeKutta5Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta3_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">RungeKutta3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_bogacki_shampine3_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">BogackiShampine3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_explicit_euler_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">ExplicitEulerIntegrator< T ></a>, and <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta2_integrator.html#a7932e0cc0f116b8a625cb025616d73ab">RungeKutta2Integrator< T ></a>.</p>
<p>Derived classes must override this function to indicate whether the integrator supports error estimation. </p>
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<p>Without error estimation, the target accuracy setting (see <aclass="el" href="classdrake_1_1systems_1_1_integrator_base.html#integrator-accuracy">accuracy settings</a>) will be unused. </p>
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<p>Implemented in <aclass="el" href="classdrake_1_1systems_1_1_velocity_implicit_euler_integrator.html#acd7fceaaf1d3c2b328b675c8d911f450">VelocityImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_implicit_euler_integrator.html#acd7fceaaf1d3c2b328b675c8d911f450">ImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_semi_explicit_euler_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">SemiExplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_radau_integrator.html#acd7fceaaf1d3c2b328b675c8d911f450">RadauIntegrator< T, num_stages ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta3_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">RungeKutta3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">RungeKutta5Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_bogacki_shampine3_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">BogackiShampine3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_explicit_euler_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">ExplicitEulerIntegrator< T ></a>, and <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta2_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">RungeKutta2Integrator< T ></a>.</p>
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<p>Implemented in <aclass="el" href="classdrake_1_1systems_1_1_velocity_implicit_euler_integrator.html#acd7fceaaf1d3c2b328b675c8d911f450">VelocityImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_implicit_euler_integrator.html#acd7fceaaf1d3c2b328b675c8d911f450">ImplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_semi_explicit_euler_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">SemiExplicitEulerIntegrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">RungeKutta5Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_radau_integrator.html#acd7fceaaf1d3c2b328b675c8d911f450">RadauIntegrator< T, num_stages ></a>, <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta3_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">RungeKutta3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_bogacki_shampine3_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">BogackiShampine3Integrator< T ></a>, <aclass="el" href="classdrake_1_1systems_1_1_explicit_euler_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">ExplicitEulerIntegrator< T ></a>, and <aclass="el" href="classdrake_1_1systems_1_1_runge_kutta2_integrator.html#a52ddb8ce13134e8e8afdfcfde6fd75ec">RungeKutta2Integrator< T ></a>.</p>
class drake::systems::RungeKutta5Integrator< T ></h3>
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<p>A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fourth order error estimate. </p>
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<p>A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fifth order error estimate. </p>
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<p>Specifically, this is an explicit Runge-Kutta method of order 5(4), where the higher order estimate is meant to be propagated (unlike the Fehlberg 4(5) method, where the 4th order solution is meant to be propagated).</p>
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<p>For a discussion of this Runge-Kutta method, see [Dormand, 1980] and [Hairer, 1993]. The embedded error estimate was derived as described in [Hairer, 1993], where all the coefficients are tabulated.</p>
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<p>The Butcher tableau for this integrator follows: </p><pre>
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<li>[Dormand, 1980] J. Dormand and P. Prince. "A family of embedded
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Runge-Kutta formulae", Journal of Computational and Applied Mathematics, 1980, 6(1): 19–26.</li>
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<li>[Hairer, 1993] E. Hairer, S. Nørsett, and G. Wanner. Solving ODEs I. 2nd rev. ed. Springer, 1993. pp. 178-9.</li>
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<li>[Fehlberg, 1969] E. Fehlberg. Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems (Vol. 315). National aeronautics and space administration, 1969.</li>
<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">A third-order Runge Kutta integrator with a third order error estimate. <ahref="classdrake_1_1systems_1_1_runge_kutta3_integrator.html#details">More...</a><br/></td></tr>
<trclass="memitem:"><tdclass="memItemLeft" align="right" valign="top">class  </td><tdclass="memItemRight" valign="bottom"><aclass="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html">RungeKutta5Integrator< T ></a></td></tr>
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<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fourth order error estimate. <ahref="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#details">More...</a><br/></td></tr>
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<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fifth order error estimate. <ahref="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#details">More...</a><br/></td></tr>
<tr id="row_289_4_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_runge_kutta3_integrator.html" target="_self">RungeKutta3Integrator< T ></a></td><td class="desc">A third-order Runge Kutta integrator with a third order error estimate </td></tr>
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<tr id="row_289_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html" target="_self">RungeKutta5Integrator< T ></a></td><td class="desc">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fourth order error estimate </td></tr>
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<tr id="row_289_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><span class="icona"><span class="icon">C</span></span><a class="el" href="classdrake_1_1systems_1_1_runge_kutta5_integrator.html" target="_self">RungeKutta5Integrator< T ></a></td><td class="desc">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fifth order error estimate </td></tr>
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<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">A third-order Runge Kutta integrator with a third order error estimate. <ahref="classdrake_1_1systems_1_1_runge_kutta3_integrator.html#details">More...</a><br/></td></tr>
<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fourth order error estimate. <ahref="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#details">More...</a><br/></td></tr>
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<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fifth order error estimate. <ahref="classdrake_1_1systems_1_1_runge_kutta5_integrator.html#details">More...</a><br/></td></tr>
<trclass="memdesc:"><tdclass="mdescLeft"> </td><tdclass="mdescRight">An element-wise hard saturation block with inputs signal <code>u</code>, saturation values \( u_{min} \) and/or \( u_{max} \), and output <code>y</code> respectively as in: <ahref="classdrake_1_1systems_1_1_saturation.html#details">More...</a><br/></td></tr>
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