More Applications of ODEs

There are a vast number of applications of ODEs in engineering.

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Notes

For more solved problems, interested reader may refer to Chaps. 3–5 of [12].

This option is not available for ode23 s, ode15i, or for implicit solvers (ode15 s, ode23t, ode23tb) applied to problems with a mass matrix.

These results can be compared with those of mass–spring systems described in Sect. 10.2. Note that similar solution patterns will be observed in both cases, hence we do not plot curves in the solution of this problem.

Note that some manufacturers use following equation in varistor modeling; \(\ln \left( v \right) = b_ <1>+ b_ \ln \left( i \right) + b_ e^\left( i \right)>> + b_ e^\left( i \right)>>\) , and they publish “b” values for each of their products.

Sir Alan L. Hodgkin (1914–1998), British physiologist.

Sir Andrew F. Huxley (1917–2012), British biophysicist. He was awarded the Nobel Prize in Physiology or Medicine in 1963 together with A. L. Hodgkin.

Richard FitzHugh (1922–2007).

Originally defined equations in [33] were \(/ = - v\left( \right)\left( \right) - w - I ,\quad / = \epsilon \left( \right)\) where \(a = 0.139\) , \(b = 1\) , \(c = 2.54\) , \(\epsilon = 0.008\) . In 1994, Rogers and McCulloch [36] modified the original model. The model parameters were also updated. In 1996, the model was further modified by Aliev and Panfilov [37] by altering the equation which modeled the change of the recovery variable and to allow for reentrant phenomena.

References [33], [34], [38] and [39] are recommended for further modeling applications in Chemical Engineering.

Such models can also be simulated using MATLAB Simulink program. Here, we do not study controlling a quadrotor behavior in response to various stimuli which is beyond the scope of this book. Interested readers may also refer to references [45,46,47].

Chaotic behavior in a pendulum can occur in cases when a pendulum is driven by some force at its pivot point, or it is a double pendulum, coupled pendulum, or magnetic pendulum (a ferromagnetic bob oscillating between magnets).

This is the expression of Kepler’s Third Law (the square of the period is proportional to the cube of the semimajor axis of the elliptic orbit.).

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Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Yeditepe University, Istanbul, Turkey Ali Ümit Keskin
  1. Ali Ümit Keskin