Abstract— Human body parts move when they are involved in an activity. In this paper an attempt is made to analyse the motion of the parts in line with the conservation of energy principle. Human body was modelled longitudinally as an inverted Quadruple pendulum. Analytical approach was adopted in analysing the potential and kinetic energies of the systems segments. The findings are consistent with the ones in the literature. Specifically, there is a positive correlation between the height of segments of the system and mechanical energy at the different segments of the system. Index Terms — Energy Conservation, Human Body Locomotion, Inverted Pendulum, Dynamical System. I. INTRODUCTION NERGY is usually release by different parts of human body, especially when involved in an activity. Energy can be defined as the capacity for doing work. Energy is the work needed to accelerate a body of a given mass from rest to its stated velocity. It may exist in a variety of forms and may be transformed from one type of energy to another.[1] However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle [2]. Total energy of an isolated system remains constant. The conservation laws are exact for an isolated system [2,3]. An isolated system implies a collection of matter which does not interact with the rest of the universe at all - and as far as we know there are really no such systems [3]. The law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time [3,4]. Energy can neither be created nor destroyed; rather, it transforms from one form to another. For instance, chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite [4]. A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind Manuscript received July 1, 2017; revised July 30, 2017. This work was supported in full by Covenant University. Energy Conservation Analysis of Human Body Locomotion Modelled as an Inverted Multi-Pendulum Dynamical System M.C. Agarana is with the Department of Mathematics, Covenant University,Nigeria,+2348023214236,michael.agarana@covenantu niversity.edu.ng .A. Ede is with the department of Civil Engineering, Covenant University Nigeria. .O. Iheanetu is with the department of Computer Science and Information System, Covenant University Nigeria. cannot exist. That is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings [4,5]. For equations of motion which do not have time translation symmetry, the conservation of energy may not be able to be defined [5]: In a hydroelectric plant, water falls from a height on to a turbine causing it to turn. The turbine turns a coil in a magnetic field, thereby generating a electric current. Therefore, potential energy of the water is converted into kinetic energy of the turbine, which is converted into electrical energy [6]. Also in a bicycle pump, mechanical energy is converted into heat energy. Thus the pump gets hot of a gas is compressed, the mechanical work done gets converted into heat energy. Alternatively, if a gas is allowed to expand, it does work and its temperature falls as its energy is used up. If we rub our hands, heat is produced due to friction. Another example is in places where there are strong winds; the winds turn the blades of a wind mill, the shaft of which turns a coil in a magnetic field, generating an electric current. Thus the energy of motion of the wind is converted into mechanical energy of the wind mill, which is converted into electrical energy as a coil is made to turn in a magnetic field.[6,7] If one knows the kinetic and potential energies that act on an object, then one can calculate the mechanical energy of the object. Imagine a roller coaster car traveling along a straight stretch of track. The car has mechanical energy because of its motion: kinetic energy [7]. The principle of conservation of energy was adopted and analysed. One way to state the conservation of energy principle is "Energy can neither be created nor destroyed".[7] Inverted pendulum is the one with its centre of mass is above its pivot point. Quadruple pendulum is like four pendulum joined together. This system is constantly unstable. In other to stabilise it some forces have to be applied. Body Mechanics plays a very important role in the movement of human body part when involved in an activity [8]. An ordinary pendulum is one with the pivot at the top and the mass at the bottom. An inverted pendulum is the opposite way round. The pivot is at the bottom and the mass is on top. The inverted pendulum is a mechanism for carrying an object form one place to another and this is how it functions during walking. The ―passenger unit‖ as Perry would call it is carried forward by the outstretched leg as it pivots over the foot [8]. So an inverted pendulum is a pendulum that has its centre of mass above its pivot point. It is often implemented with the pivot point mounted on a moving body that can move horizontally. Unlike a normal pendulum which is always stable when hanging downwards, an inverted pendulum is E Energy Conservation Analysis of Human Body Locomotion Modelled as an Inverted Quadruple Pendulum Dynamical System Michael C. Agarana, IAENG Member, Anthony Ede and Olamma Iheanetu Proceedings of the World Congress on Engineering and Computer Science 2017 Vol II WCECS 2017, October 25-27, 2017, San Francisco, USA ISBN: 978-988-14048-4-8 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCECS 2017