International Journal of New Technology and Research (IJNTR) ISSN:2454-4116, Volume-2, Issue-10, October 2016 Pages 45-51 45 www.ijntr.org Abstract—As it is well known, nanorobotics is the field that deals with the controlled manipulation with atomic and molecular-sized objects. In order to control nanorobots in the regions of mechanics, electronics, electromagnetism, photonics and biomaterials we have to have the ability to construct of the related artificial control potential fields. At the nanoscale the control dynamics is very complex because there are very strong interactions between nanorobots, manipulated objects and nanoenvironment. The problem is to design the control dynamics that will compensate or/and control the mentioned interactions. The first step in designing of the control dynamics for nanorobots is the development of the relativistic Hamiltonian (Hamilton functions) that will include external artificial control potential fields. Thus, derivation of the first and second form of the relativistic Hamiltonians for nanorobots control is presented in this paper. Index Terms — Nanorobotics, Relativistic Hamiltonian, Multipotential field, Artificial control field. I. INTRODUCTION As it is well known, the nanorobotics belongs to the multidisciplinary field that deals with the controlled manipulation with atomic and molecular-sized objects and therefore sometimes is called molecular robotics 1-10. Potential applications of the nanorobots are expected in the tree important regions: nanomedicine, nanotechnology and space applications. In nanomedicine the nanorobots can be employed for surgery, early diagnoses, drug delivery at the right place (for destroying a cancer cell), biomedical instrumentation, pharmacokinetics, monitoring of diabetes and genome applications by reading and manipulating DNA 7. In nanotechnology the nanorobots can be utilized for creation of new materials, nanofabrics for different products, cell probes with small dimensions, computer memory, near field optics, x-ray fabrication, very small batteries and optical antennas. In the space applications it is expected that nanorobots replace of human being in the intergalactic space missions, be hardware and software to fly on satellites and have a high level of an artificial intelligence. The complex tasks of the future nanorobots are sensing, thinking, acting and working cooperatively with the other nanorobots. In order to control nanorobots in mechanics, electronics, electromagnetic, photonics, chemical and biomaterials regions we have to have the ability to construct the related artificial control potential fields. At the nanoscale the control dynamics is very complex because there are very strong interaction between nano robots and nanoenvironment. Thus, the first step in designing the control dynamics for nanorobots Branko Novakovic, Dubravko Majetic, Josip Kasac, Danko Brezak, FSB – University of Zagreb, Luciceva 5, P.O.B. 509, 10000 Zagreb, Croatia, \ is the development of the relativistic Hamiltonian that will include external artificial potential field. This paper has been written by consideration of the related theories and fundamental laws of physics in 11-21 and 30-37. The generally approach to the multidisciplinary nanorobotics field has been presented in 22-23. In the derivation of the Hamiltonians that includes the external potential fields for control in nanorobotics, the new General Lorentz Transformation model (the GLT α model derived in 24-26) and the new Relativistic Alpha Field Theory (RAFT) in 27- 29 are employed. The first form of the Hamilton function has been derived starting with variation principle and using the procedure from [31-[32]. In that sense, the relativistic invariant term Ldt (where L is the Lagrange function and dt is the differential of the time) is derived by employing product of the two relativistic invariant terms: proper time dτ and energetic term m o c 2 . Here m o is a rest mass of a sample (particle) and c is the speed of the light in a vacuum. It is shown that the relativistic invariant term Ldt can also be derived starting with the generalized line element ds, since ds 2 is a fundamental invariant of the four dimensional space-time continuum. The obtained first form of the Hamiltonian H is equal to the general covariant energy equation E c that usually can be derived by employing the null component of the covariant four-momentum vector P o . Further, this form of the Hamiltonian can be easily transformed into the expression that includes extended momentum as a function of the field parameters α and α′. This form is also very important, because the obtained Hamiltonian is a linear function of the extended momentum and therefore belongs to the Dirac’s like structure of the Hamiltonian [16]-[17]. The obtained result gives the possibility to compare the coefficients of the well known Dirac’s Hamiltonian and the first form of the Hamiltonian derived in this paper. The second form of the Hamiltonian H has been derived starting with the modification of the some relations in the previous derivation procedure. This form of the Hamiltonian belongs to the usual structure of the classical relativistic Hamiltonians [36]-[37]. The main shortage of the second form of the Hamiltonian is the fact that this form is a nonlinear function of the extended momentum. Thus, the first form of the Hamiltonian has got the important priority, because this form is linear function of the extended momentum. Usually, one can introduce the approximation of the second form of the Hamiltonian. It also has been done in this paper and resulted with the new form of the Hamiltonian as the approximation of its second form. This paper is organized as follows. The second section presents a process of the determination of the dimensionless field parameters α and α′. It is shown that these parameters are functions of the potential energy of the multi-potential field with n-potentials plus an artificial control field of the nanorobot control. The third section shows the derivation of Hamiltonian of Multipotential Field in Nanorobotics Branko Novakovic, Dubravko Majetic, Josip Kasac, Danko Brezak