There is an old standing problem of radiation reaction     consisting mainly in the that the usual approach, based on expressing the radiation reaction force in terms of the third time differentiation of the position of the charged particle, brings about of what is called a pre-acceleration of the charged particle even if there is not external force at all. However, experimentally one sees that as soon the external force is zero, the acceleration of the charged particle is zero too, and emission of electromagnetic radiation stops. This experimental fact led to propose an alternative approach  to the radiation reaction force. This new approach is based on expressing the radiation reaction force in terms of the external force acting on the charged particle, responsible for its acceleration. Although, this approach seems to point in the right direction, experimental verification of this theoretical idea is required. In reference  , the approach was implemented for linear and circular acceleration of a charged particle. In this paper, a generalization of the idea is carried out, using the same method pre- sented in that paper, and the generalization takes the same form as Equatioin (1), but with the additional radiation reaction force term.
2. Acceleration and Force Relation
The relativistic equation to describe the motion of a charge particle under an external force is given by 
where and are the mass and the velocity of the charged particle, and is the usual relativistic time dilation factor
being the speed of the charged particle in units of the speed of light “c”,
Making the differentiation in (1), this equation can be written as
where . Inverting this matrix and making some rearrangements, it follows that
where is the matrix
This is the expression with makes the relation between the normalized acceleration with the external force.
3. Radiation Reaction Force
It is well known that the power radiated per solid angle of an accelerated charged particle of charge “q” is 
where is the unitary vector that goes from the position of the charge at the retarded time ( ) to the observer position. So, using (5) on this expres- sion, it follows that
Integrating with respect the solid angle and with respect the time in the inter- val , the energy radiated by the charged particle during this time is
which can be written in terms of angles as
where is the unitary vector in the direction and is the unitary vector in the direction , is the angle between the vectors and , and is the angle between the vectors and . One can choose our reference system such that be the angle related with the solid angle coordinates. The angles and depend on the solid angle coordinates ( ).
Assume now that this energy lost is due to the work done by a nonconser- vative radiation reaction force, to move the charged particle from the position a the time , to the position at the time t. So, one would have
However, one has that . Then, it follows that
Equaling (10) and (12), and since the resulting expression is valid for any time intervale on the real line, one obtains
where is the charged particle speed and is the angle between the vectors and . Since must represent a force causing damping on the motion of the charged particle, must point on the direction, where , meaning the the angle between and must be . There- fore, one gets the following expression for radiation reaction force
In this way, the modified relativistic equation of motion of a charged particle under an arbitrary external force is
where the radiation reaction force term has been added to the expression (1), or it can be written, using (14), as
One must point out that if the external force is zero, the radiation reac- tion force is also zero, and noncausal preacceleration is absent since the charged particle will have constant velocity, as the experiments indicate so far.
4. Special Cases
As one can see from expression (14), the integration over the solid angle is not in general a trivial matter, and numerical integration may be required. However, there are two cases where this integration can be done without any difficulty, and these cases are presented below.
a) Linear acceleration case: In this case one has that is parallel to ( ) and there is not dependence on , this integration is well known  , and choosing and , the resulting equation is
where , and is defined as
This equation is the same as that proposed for this case in reference  .
b) Circular acceleration case: In this case one has that and are ortho- gonal. The integration is also well known  , and choosing and , one arrives to the following equation
where , , and the motion is reduced to the plane (x,y). This expression is the same as that one proposed on reference  .
Following the same approach of reference  , a generalization has been formu- lated for the force approach to radiation reaction, expression (16). This genera- lization has the same main property of the force approach, wherever the external force is zero, the acceleration of the charged particle is zero, and the radiation reaction force is zero too, and non pre-acceleration concept will appear here.
 Jackson, J.D. (2007) Comment on “Preacceleration without radiation: The nonexistence of preradiation phenomenon,” by J. A. Heras [Am. J. Phys. 74 (11), 1025-1030 (2006)]. American Journal of Physics, 75, 844.
 Hnizdo, V. (2007) Comment on “Preacceleration without radiation: The nonexistence of preradiation phenomenon,” by J. A. Heras [Am. J. Phys. 74 (11), 1025-1030 (2006)]. American Journal of Physics, 75, 845.