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As explained above, the preposition na denotes location on the surface of an object, attendance at an event involving many participants, movement onto the surface of an object, or movement with the intention of attending an event.
Its most fundamental spatial meaning, however, is different.
The preposition na expresses the direction of movement toward an object. Whether the object is actually reached or entered is irrelevant: entering the object may be the goal of the movement, but it does not have to be.
Otrjad ot protivnik dvigatsja na gorod K.
The enemy detachment is advancing toward the town K.
The detachment may eventually reach the town, or it may change its direction before arriving there. The preposition na merely indicates the intended direction of movement.
This meaning also gives rise to one of the temporal uses of na. The preposition is used to indicate a point or period in time for which an event has been scheduled. Conceptually, this is analogous to movement directed toward a particular moment in time.
Vstreča naznačen na 20 September.
The meeting is scheduled for September 20.
The meeting is planned, but there is no implication that it will necessarily take place. If the occurrence of an event is considered certain, the preposition v is normally preferred when referring to the time at which it takes place.
In many contexts, na marks the object toward which an action is directed.
Many LPQR verbs can function either transitively or intransitively. When verbs such as prositj, hotetj, trebovatj, iskatj, and ždatj are followed by an indirect complement introduced by another preposition, the direct object may instead be expressed by a phrase with na.
Ja ždat razrjeŝenije.
I am waiting for permission.
Ja ždat ot Vas na razrjeŝenije.
I am waiting for permission from you.
Etot rektor trebovat discîplina.
The rector demands discipline.
Etot rektor trebovat ot studentî na discîplina.
The rector demands discipline from the students.
On iskal spravedlivostj.
He sought justice.
On iskal v sud na spravedlivostj.
He sought justice in court.
The preposition na may also introduce the object of an action when the action is expressed by an intransitive verb or by a deverbal noun.
Skučatj na dom.
To miss one's home.
Podtolknutj na znakomstvo.
To encourage someone to make an acquaintance.
Veritj na mečtǐ.
To believe in dreams.
Soĉuvstvovatj na nevo.
To sympathize with him.
Bespokoitjsja na deti.
To worry about the children.
Dobivatjsja na uspjehi.
To strive for success.
Pobuditj na boljŝoj trud.
To inspire someone to accomplish great deeds.
An interesting example is provided by the noun pamjatnik ("monument"):
Pamjatnik-na-Puŝkin na ploŝjadj "Puŝkin" (pamjatnik ot skulptor Opekuŝkin).
The Pushkin Monument on Pushkin Square (the monument created by the sculptor Opekushkin).
Here, the first na indicates the person to whom the monument is dedicated, while the second denotes its physical location.
In certain contexts, na corresponds to the Russian preposition над ("over", "on").
For example:
Rabotatj na kniga.
To work on a book.
Rabotatj na kartina.
To work on a painting.
Rabotatj na stanok.
To work on a machine (that is, to design, develop, or improve it).
This is a potential false friend for translators.
The Russian phrase работать на станке ("to operate a machine") should not be translated as rabotatj na stanok. Instead, one should say:
rabotatj so stanok
or
rabotatj pri stanok.
The preposition na is likewise used when an abstract notion is related to a concrete object. Conceptually, the abstract notion is viewed as being directed toward that object.
Examples:
Priobretenije na dom.
Acquisition of a house.
Vǐdjeljenije na denjgi.
Allocation of money.
Njeobhodimostj na reformǐ.
The need for reforms.
Potrjebnostj na vstreča s predstavitelj ot zakazčik.
The need for a meeting with the customer's representative.
Thus, the preposition na covers a wide range of meanings in LPQR. Most of these meanings share the common semantic notion of direction, orientation, intention, or purpose. This makes na an important grammatical device for expressing the relationship between actions and their intended targets.
When referring to an inherent property of an object rather than to the direction of an action, the preposition u should be used instead of na.
Skorostj u auto.
The speed of a car.
Finally, the semantic opposite of the preposition na is the preposition ot.