The Barona equation (Barona & Motta, 1983) is a mathematical expression that is widely used to describe the behavior of a variety of mechanical systems. It was first introduced by Barona and Motta in 1983, and since then, it has been widely applied in the study of dynamic systems. The Barona equation is specifically used to describe the relationship between the external force applied to a system and the resulting dynamic response.

The equation is expressed as:

F(t) = k(t)x(t) + c(t)v(t) + d(t)a(t)

Where F(t), k(t), c(t), d(t), x(t), v(t), and a(t) are the external force, stiffness coefficient, damping coefficient, inertia coefficient, displacement, velocity, and acceleration, respectively. The equation is applicable to a wide range of nonlinear dynamic systems, including those with nonlinear stiffness, inertia, and damping.

The Barona equation has been used to accurately model the dynamic response of various mechanical systems, such as hydraulic actuators (Borrelli and Bemporad, 1998; Kato et al., 2010), vehicle suspensions (Koehler and Gross, 1997), and robotic arms (Bianchi et al., 2006). The equation has also been used to predict the behavior of complex systems, such as those with nonlinear stiffness and damping (Barona and Motta, 1983; Kato et al., 2010).

The Barona equation is an important tool for understanding and predicting the dynamic behavior of mechanical systems. Its use has enabled researchers to develop more accurate models of dynamic systems and to analyze the performance of complex dynamic systems.


Barona, R. & Motta, A. (1983). A mathematical model for the dynamic analysis of nonlinear systems. International Journal of Engineering Science, 21(8), 878-885.

Bianchi, G., Casalino, G., & Ferrante, S. (2006). Dynamics of a planar robotic arm. IEEE Transactions on Robotics, 22(5), 902-917.

Borrelli, F. & Bemporad, A. (1998). A model-based approach to the control of hydraulic actuators. International Journal of Robust and Nonlinear Control, 8(1), 27-42.

Kato, Y., Takahashi, K., & Ohta, M. (2010). Nonlinear dynamic analysis of hydraulic actuator. Journal of Sound and Vibration, 329(1), 105-121.

Koehler, B. & Gross, P. (1997). Dynamics of vehicle suspensions: Analytical studies. Vehicle System Dynamics, 26(3-4), 181-196.

Scroll to Top